From 1427fe34f0bf364f860b9f3c4ecd811215e0cdcb Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 19:22:41 +0530
Subject: [PATCH 01/19] avg and mps speed formulae added

---
 ...avg_and_mps_speeds_of_gaseous_molecules.py | 79 +++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100644 physics/avg_and_mps_speeds_of_gaseous_molecules.py

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
new file mode 100644
index 000000000000..70f189b91912
--- /dev/null
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -0,0 +1,79 @@
+"""
+The root-mean-square, average and most probable speeds are derived from the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a probability distribution that describes the distribution of speeds for particles in a gas. The distribution is given by the following equation:
+    
+        -------------------------------------------------
+        | f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
+        -------------------------------------------------
+        
+where:
+    f(v) is the fraction of molecules with a speed v
+    M is the molar mass of the gas in kg/mol
+    R is the gas constant
+    T is the absolute temperature
+
+More information about the Maxwell-Boltzmann distribution can be found here: https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
+    
+The average speed can be calculated by integrating the Maxwell-Boltzmann distribution from 0 to infinity and dividing by the total number of molecules. The result is:
+        
+        ---------------------
+        | vavg = √8RT/πM    |
+        ---------------------
+        
+The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v and setting the result equal to zero. The result is:
+
+        ---------------------
+        | vmp = √2RT/M      |
+        ---------------------
+        
+The root-mean-square speed is another measure of the average speed of the molecules in a gas. It is calculated by taking the square root of the average of the squares of the speeds of the molecules. The result is:
+
+        ---------------------
+        | vrms = √3RT/m     |
+        ---------------------
+
+Here we have defined functions to calculate the average and most probable speeds of molecules in a gas given the temperature and molar mass of the gas.
+"""
+
+# necessary constants
+PI = 3.1415926535 # pi
+R = 8.3144626181 # gas constant
+
+def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
+    """
+    Takes the temperature (in K) and molar mass (in kg/mol) of a gas and returns the average speed of a molecule in the gas (in m/s).
+    
+    Examples:
+    >>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K
+    454.34887551126405
+    >>> avg_speed_of_molecule(300, 0.032) # oxygen at 300 K
+    445.5257273482451
+    """
+    if temperature < 0:
+        raise Exception("Absolute temperature cannot be less than 0 K")
+    if molar_mass <= 0:
+        raise Exception("Molar mass should be greater than 0 kg/mol")
+    else:
+        return (8 * R * temperature / (PI * molar_mass)) ** 0.5
+    
+def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
+    """
+    Takes the temperature (in K) and molar mass (in kg/mol) of a gas and returns the most probable speed of a molecule in the gas (in m/s).
+    
+    Examples:
+    >>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K
+    402.6562070215111
+    >>> mps_speed_of_molecule(300, 0.032) # oxygen at 300 K
+    394.83689555229637
+    """
+    if temperature < 0:
+        raise Exception("Absolute temperature cannot be less than 0 K")
+    if molar_mass <= 0:
+        raise Exception("Molar mass should be greater than 0 kg/mol")
+    else:
+        return (2 * R * temperature / molar_mass) ** 0.5
+    
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    
\ No newline at end of file

From 0608c40a89a1cba314551633795318f140466825 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 10 Oct 2023 14:00:21 +0000
Subject: [PATCH 02/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 ...avg_and_mps_speeds_of_gaseous_molecules.py | 28 ++++++++++---------
 1 file changed, 15 insertions(+), 13 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index 70f189b91912..b851ae3e2542 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -1,10 +1,10 @@
 """
 The root-mean-square, average and most probable speeds are derived from the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a probability distribution that describes the distribution of speeds for particles in a gas. The distribution is given by the following equation:
-    
+
         -------------------------------------------------
         | f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
         -------------------------------------------------
-        
+
 where:
     f(v) is the fraction of molecules with a speed v
     M is the molar mass of the gas in kg/mol
@@ -12,19 +12,19 @@
     T is the absolute temperature
 
 More information about the Maxwell-Boltzmann distribution can be found here: https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
-    
+
 The average speed can be calculated by integrating the Maxwell-Boltzmann distribution from 0 to infinity and dividing by the total number of molecules. The result is:
-        
+
         ---------------------
         | vavg = √8RT/πM    |
         ---------------------
-        
+
 The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v and setting the result equal to zero. The result is:
 
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
-        
+
 The root-mean-square speed is another measure of the average speed of the molecules in a gas. It is calculated by taking the square root of the average of the squares of the speeds of the molecules. The result is:
 
         ---------------------
@@ -35,13 +35,14 @@
 """
 
 # necessary constants
-PI = 3.1415926535 # pi
-R = 8.3144626181 # gas constant
+PI = 3.1415926535  # pi
+R = 8.3144626181  # gas constant
+
 
 def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
     Takes the temperature (in K) and molar mass (in kg/mol) of a gas and returns the average speed of a molecule in the gas (in m/s).
-    
+
     Examples:
     >>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K
     454.34887551126405
@@ -54,11 +55,12 @@ def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
         raise Exception("Molar mass should be greater than 0 kg/mol")
     else:
         return (8 * R * temperature / (PI * molar_mass)) ** 0.5
-    
+
+
 def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
     Takes the temperature (in K) and molar mass (in kg/mol) of a gas and returns the most probable speed of a molecule in the gas (in m/s).
-    
+
     Examples:
     >>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K
     402.6562070215111
@@ -71,9 +73,9 @@ def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
         raise Exception("Molar mass should be greater than 0 kg/mol")
     else:
         return (2 * R * temperature / molar_mass) ** 0.5
-    
+
+
 if __name__ == "__main__":
     import doctest
 
     doctest.testmod()
-    
\ No newline at end of file

From 7457b25d709d242468b8d31b29307dee3914771d Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 19:33:39 +0530
Subject: [PATCH 03/19] avg and mps speed formulae added

---
 ...avg_and_mps_speeds_of_gaseous_molecules.py | 37 ++++++++++++-------
 1 file changed, 24 insertions(+), 13 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index 70f189b91912..8ee71c56f903 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -1,5 +1,8 @@
 """
-The root-mean-square, average and most probable speeds are derived from the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a probability distribution that describes the distribution of speeds for particles in a gas. The distribution is given by the following equation:
+The root-mean-square, average and most probable speeds are derived from 
+the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a 
+probability distribution that describes the distribution of speeds for particles in a gas.
+The distribution is given by the following equation:
     
         -------------------------------------------------
         | f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
@@ -11,27 +14,34 @@
     R is the gas constant
     T is the absolute temperature
 
-More information about the Maxwell-Boltzmann distribution can be found here: https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
+More information about the Maxwell-Boltzmann distribution can be found here: 
+https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
     
-The average speed can be calculated by integrating the Maxwell-Boltzmann distribution from 0 to infinity and dividing by the total number of molecules. The result is:
+The average speed can be calculated by integrating the Maxwell-Boltzmann distribution 
+from 0 to infinity and dividing by the total number of molecules. The result is:
         
         ---------------------
         | vavg = √8RT/πM    |
         ---------------------
         
-The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v and setting the result equal to zero. The result is:
+The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. 
+This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v 
+and setting the result equal to zero. The result is:
 
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
         
-The root-mean-square speed is another measure of the average speed of the molecules in a gas. It is calculated by taking the square root of the average of the squares of the speeds of the molecules. The result is:
+The root-mean-square speed is another measure of the average speed of the molecules in a gas. 
+It is calculated by taking the square root of the average of the 
+squares of the speeds of the molecules. The result is:
 
         ---------------------
         | vrms = √3RT/m     |
         ---------------------
 
-Here we have defined functions to calculate the average and most probable speeds of molecules in a gas given the temperature and molar mass of the gas.
+Here we have defined functions to calculate the average and 
+most probable speeds of molecules in a gas given the temperature and molar mass of the gas.
 """
 
 # necessary constants
@@ -40,8 +50,9 @@
 
 def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
-    Takes the temperature (in K) and molar mass (in kg/mol) of a gas and returns the average speed of a molecule in the gas (in m/s).
-    
+    Takes the temperature (in K) and molar mass (in kg/mol) of a gas 
+    and returns the average speed of a molecule in the gas (in m/s).
+
     Examples:
     >>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K
     454.34887551126405
@@ -54,11 +65,12 @@ def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
         raise Exception("Molar mass should be greater than 0 kg/mol")
     else:
         return (8 * R * temperature / (PI * molar_mass)) ** 0.5
-    
+
 def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
-    Takes the temperature (in K) and molar mass (in kg/mol) of a gas and returns the most probable speed of a molecule in the gas (in m/s).
-    
+    Takes the temperature (in K) and molar mass (in kg/mol) of a gas 
+    and returns the most probable speed of a molecule in the gas (in m/s).
+
     Examples:
     >>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K
     402.6562070215111
@@ -71,9 +83,8 @@ def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
         raise Exception("Molar mass should be greater than 0 kg/mol")
     else:
         return (2 * R * temperature / molar_mass) ** 0.5
-    
+
 if __name__ == "__main__":
     import doctest
 
     doctest.testmod()
-    
\ No newline at end of file

From b1ef5a36fbec003505091eda2731e3bb8aca4955 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 19:39:08 +0530
Subject: [PATCH 04/19] fixed_spacing

---
 physics/avg_and_mps_speeds_of_gaseous_molecules.py | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index 8ee71c56f903..20baff29082e 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -3,11 +3,11 @@
 the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a 
 probability distribution that describes the distribution of speeds for particles in a gas.
 The distribution is given by the following equation:
-    
+
         -------------------------------------------------
         | f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
         -------------------------------------------------
-        
+   
 where:
     f(v) is the fraction of molecules with a speed v
     M is the molar mass of the gas in kg/mol
@@ -16,14 +16,14 @@
 
 More information about the Maxwell-Boltzmann distribution can be found here: 
 https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
-    
+
 The average speed can be calculated by integrating the Maxwell-Boltzmann distribution 
 from 0 to infinity and dividing by the total number of molecules. The result is:
-        
+ 
         ---------------------
         | vavg = √8RT/πM    |
         ---------------------
-        
+
 The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. 
 This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v 
 and setting the result equal to zero. The result is:
@@ -31,7 +31,7 @@
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
-        
+
 The root-mean-square speed is another measure of the average speed of the molecules in a gas. 
 It is calculated by taking the square root of the average of the 
 squares of the speeds of the molecules. The result is:

From 07502c875b13e28836d1e1769613d192ce87bf74 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 10 Oct 2023 14:11:38 +0000
Subject: [PATCH 05/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 ...avg_and_mps_speeds_of_gaseous_molecules.py | 29 ++++++++++---------
 1 file changed, 15 insertions(+), 14 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index f861520d334b..8dfaa9bd9944 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -1,46 +1,46 @@
 """
-The root-mean-square, average and most probable speeds are derived from 
-the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a 
+The root-mean-square, average and most probable speeds are derived from
+the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a
 probability distribution that describes the distribution of speeds for particles in a gas.
 The distribution is given by the following equation:
 
         -------------------------------------------------
         | f(v) = (M/2πRT)^(3/2) * 4πv^2 * e^(-Mv^2/2RT) |
         -------------------------------------------------
-   
+
 where:
     f(v) is the fraction of molecules with a speed v
     M is the molar mass of the gas in kg/mol
     R is the gas constant
     T is the absolute temperature
 
-More information about the Maxwell-Boltzmann distribution can be found here: 
+More information about the Maxwell-Boltzmann distribution can be found here:
 https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
 
-The average speed can be calculated by integrating the Maxwell-Boltzmann distribution 
+The average speed can be calculated by integrating the Maxwell-Boltzmann distribution
 from 0 to infinity and dividing by the total number of molecules. The result is:
- 
+
         ---------------------
         | vavg = √8RT/πM    |
         ---------------------
 
-The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. 
-This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v 
+The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum.
+This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v
 and setting the result equal to zero. The result is:
 
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
 
-The root-mean-square speed is another measure of the average speed of the molecules in a gas. 
-It is calculated by taking the square root of the average of the 
+The root-mean-square speed is another measure of the average speed of the molecules in a gas.
+It is calculated by taking the square root of the average of the
 squares of the speeds of the molecules. The result is:
 
         ---------------------
         | vrms = √3RT/m     |
         ---------------------
 
-Here we have defined functions to calculate the average and 
+Here we have defined functions to calculate the average and
 most probable speeds of molecules in a gas given the temperature and molar mass of the gas.
 """
 
@@ -51,7 +51,7 @@
 
 def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
-    Takes the temperature (in K) and molar mass (in kg/mol) of a gas 
+    Takes the temperature (in K) and molar mass (in kg/mol) of a gas
     and returns the average speed of a molecule in the gas (in m/s).
 
     Examples:
@@ -67,9 +67,10 @@ def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     else:
         return (8 * R * temperature / (PI * molar_mass)) ** 0.5
 
+
 def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
-    Takes the temperature (in K) and molar mass (in kg/mol) of a gas 
+    Takes the temperature (in K) and molar mass (in kg/mol) of a gas
     and returns the most probable speed of a molecule in the gas (in m/s).
 
     Examples:
@@ -85,8 +86,8 @@ def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     else:
         return (2 * R * temperature / molar_mass) ** 0.5
 
+
 if __name__ == "__main__":
     import doctest
 
     doctest.testmod()
-

From ead4f47af540c24a9575fa1eda95897bec18a76b Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 19:44:07 +0530
Subject: [PATCH 06/19] spacing

---
 .../avg_and_mps_speeds_of_gaseous_molecules.py | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index f861520d334b..3b7e622184e7 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -1,7 +1,8 @@
 """
 The root-mean-square, average and most probable speeds are derived from 
 the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a 
-probability distribution that describes the distribution of speeds for particles in a gas.
+probability distribution that describes the distribution of speeds for particles 
+in a gas.
 The distribution is given by the following equation:
 
         -------------------------------------------------
@@ -24,24 +25,25 @@
         | vavg = √8RT/πM    |
         ---------------------
 
-The most probable speed is the speed at which the Maxwell-Boltzmann distribution is at its maximum. 
-This can be found by differentiating the Maxwell-Boltzmann distribution with respect to v 
-and setting the result equal to zero. The result is:
+The most probable speed is the speed at which the Maxwell-Boltzmann distribution 
+is at its maximum. This can be found by differentiating the Maxwell-Boltzmann 
+distribution with respect to v and setting the result equal to zero. The result is:
 
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
 
-The root-mean-square speed is another measure of the average speed of the molecules in a gas. 
-It is calculated by taking the square root of the average of the 
-squares of the speeds of the molecules. The result is:
+The root-mean-square speed is another measure of the average speed 
+of the molecules in a gas. It is calculated by taking the square root 
+of the average of the squares of the speeds of the molecules. The result is:
 
         ---------------------
         | vrms = √3RT/m     |
         ---------------------
 
 Here we have defined functions to calculate the average and 
-most probable speeds of molecules in a gas given the temperature and molar mass of the gas.
+most probable speeds of molecules in a gas given the 
+temperature and molar mass of the gas.
 """
 
 # necessary constants

From cb006c383bbba43063a51f079f47a528900230a8 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 10 Oct 2023 14:19:02 +0000
Subject: [PATCH 07/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 .../avg_and_mps_speeds_of_gaseous_molecules.py | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index 2a7fd542289d..3157741208e9 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -1,7 +1,7 @@
 """
-The root-mean-square, average and most probable speeds are derived from 
-the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a 
-probability distribution that describes the distribution of speeds for particles 
+The root-mean-square, average and most probable speeds are derived from
+the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a
+probability distribution that describes the distribution of speeds for particles
 in a gas.
 The distribution is given by the following equation:
 
@@ -25,24 +25,24 @@
         | vavg = √8RT/πM    |
         ---------------------
 
-The most probable speed is the speed at which the Maxwell-Boltzmann distribution 
-is at its maximum. This can be found by differentiating the Maxwell-Boltzmann 
+The most probable speed is the speed at which the Maxwell-Boltzmann distribution
+is at its maximum. This can be found by differentiating the Maxwell-Boltzmann
 distribution with respect to v and setting the result equal to zero. The result is:
 
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
 
-The root-mean-square speed is another measure of the average speed 
-of the molecules in a gas. It is calculated by taking the square root 
+The root-mean-square speed is another measure of the average speed
+of the molecules in a gas. It is calculated by taking the square root
 of the average of the squares of the speeds of the molecules. The result is:
 
         ---------------------
         | vrms = √3RT/m     |
         ---------------------
 
-Here we have defined functions to calculate the average and 
-most probable speeds of molecules in a gas given the 
+Here we have defined functions to calculate the average and
+most probable speeds of molecules in a gas given the
 temperature and molar mass of the gas.
 """
 

From ab04734aa2ec0ef0af14fc5e233d3067da27eb3c Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 19:50:16 +0530
Subject: [PATCH 08/19] ws

---
 .../avg_and_mps_speeds_of_gaseous_molecules.py | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
index 2a7fd542289d..3157741208e9 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/avg_and_mps_speeds_of_gaseous_molecules.py
@@ -1,7 +1,7 @@
 """
-The root-mean-square, average and most probable speeds are derived from 
-the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a 
-probability distribution that describes the distribution of speeds for particles 
+The root-mean-square, average and most probable speeds are derived from
+the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a
+probability distribution that describes the distribution of speeds for particles
 in a gas.
 The distribution is given by the following equation:
 
@@ -25,24 +25,24 @@
         | vavg = √8RT/πM    |
         ---------------------
 
-The most probable speed is the speed at which the Maxwell-Boltzmann distribution 
-is at its maximum. This can be found by differentiating the Maxwell-Boltzmann 
+The most probable speed is the speed at which the Maxwell-Boltzmann distribution
+is at its maximum. This can be found by differentiating the Maxwell-Boltzmann
 distribution with respect to v and setting the result equal to zero. The result is:
 
         ---------------------
         | vmp = √2RT/M      |
         ---------------------
 
-The root-mean-square speed is another measure of the average speed 
-of the molecules in a gas. It is calculated by taking the square root 
+The root-mean-square speed is another measure of the average speed
+of the molecules in a gas. It is calculated by taking the square root
 of the average of the squares of the speeds of the molecules. The result is:
 
         ---------------------
         | vrms = √3RT/m     |
         ---------------------
 
-Here we have defined functions to calculate the average and 
-most probable speeds of molecules in a gas given the 
+Here we have defined functions to calculate the average and
+most probable speeds of molecules in a gas given the
 temperature and molar mass of the gas.
 """
 

From 6a741dc63f7ba3140c24e2cf7bde364b9ae4afa2 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 20:37:45 +0530
Subject: [PATCH 09/19] added amicable numbers

---
 maths/amicable_pair.py | 65 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 65 insertions(+)
 create mode 100644 maths/amicable_pair.py

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
new file mode 100644
index 000000000000..d596cfc9884b
--- /dev/null
+++ b/maths/amicable_pair.py
@@ -0,0 +1,65 @@
+"""
+Amicable numbers are two different natural numbers such that the sum
+of the proper divisors of each is equal to the other number.
+That is, s(a)=b and s(b)=a, where s(n) is equal to
+the sum of positive divisors of n except n itself.
+Here, a and b form a pair of amicable numbers.
+
+More information about amicable numbers can be found here:
+https://en.wikipedia.org/wiki/Amicable_numbers
+
+Here, we have defined a function to check if two numbers are amicable.
+We have also defined an auxiliary function,
+to find the sum of the proper divisors of a number.
+"""
+
+def sum_of_divisors(n: int) -> int:
+    """
+    Find the sum of the proper divisors of a number.
+    
+    Examples:
+    >>> sum_of_divisors(220)
+    284
+    >>> sum_of_divisors(284)
+    220
+    """
+    sum = 0
+    for i in range(1, n):
+        if n % i == 0:
+            sum += i
+    
+    return sum
+
+def is_amicable_pair(a: int, b: int) -> bool:
+    """
+    Check if two numbers (a and b) are amicable numbers.
+    Arguments must be positive integers.
+    
+    Examples:
+    >>> is_amicable_pair(220, 284)
+    True
+    >>> is_amicable_pair(1184, 1210)
+    True
+    >>> is_amicable_pair(127, 729)
+    False
+    >>> is_amicable_pair(7, 13)
+    False
+    >>> is_amicable_pair(0, 12)
+    Traceback (most recent call last):
+        ...
+    ValueError: Numbers must be positive integers.
+    >>> is_amicable_pair(12, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Numbers must be positive integers.
+    >>> is_amicable_pair(42, 42)
+    False
+    """
+    if a <= 0 or b <= 0:
+        raise ValueError("Numbers must be positive integers.")
+
+    return sum_of_divisors(a) == b and sum_of_divisors(b) == a
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
\ No newline at end of file

From d13c09d2ca2399abd3126a3a63584dc5f308d582 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 10 Oct 2023 15:08:24 +0000
Subject: [PATCH 10/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/amicable_pair.py | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
index d596cfc9884b..a94dcab32fee 100644
--- a/maths/amicable_pair.py
+++ b/maths/amicable_pair.py
@@ -13,10 +13,11 @@
 to find the sum of the proper divisors of a number.
 """
 
+
 def sum_of_divisors(n: int) -> int:
     """
     Find the sum of the proper divisors of a number.
-    
+
     Examples:
     >>> sum_of_divisors(220)
     284
@@ -27,14 +28,15 @@ def sum_of_divisors(n: int) -> int:
     for i in range(1, n):
         if n % i == 0:
             sum += i
-    
+
     return sum
 
+
 def is_amicable_pair(a: int, b: int) -> bool:
     """
     Check if two numbers (a and b) are amicable numbers.
     Arguments must be positive integers.
-    
+
     Examples:
     >>> is_amicable_pair(220, 284)
     True
@@ -60,6 +62,8 @@ def is_amicable_pair(a: int, b: int) -> bool:
 
     return sum_of_divisors(a) == b and sum_of_divisors(b) == a
 
+
 if __name__ == "__main__":
     import doctest
-    doctest.testmod()
\ No newline at end of file
+
+    doctest.testmod()

From 63734b9d97e34ec9d31f34d196f4d24099911ad4 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 20:41:56 +0530
Subject: [PATCH 11/19] added amicable numbers

---
 maths/amicable_pair.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
index d596cfc9884b..144d7e2a42ae 100644
--- a/maths/amicable_pair.py
+++ b/maths/amicable_pair.py
@@ -13,7 +13,7 @@
 to find the sum of the proper divisors of a number.
 """
 
-def sum_of_divisors(n: int) -> int:
+def sum_of_divisors(number: int) -> int:
     """
     Find the sum of the proper divisors of a number.
     
@@ -24,15 +24,15 @@ def sum_of_divisors(n: int) -> int:
     220
     """
     sum = 0
-    for i in range(1, n):
-        if n % i == 0:
+    for i in range(1, number):
+        if number % i == 0:
             sum += i
     
     return sum
 
-def is_amicable_pair(a: int, b: int) -> bool:
+def is_amicable_pair(number_1: int, number_2: int) -> bool:
     """
-    Check if two numbers (a and b) are amicable numbers.
+    Check if two numbers (number_1 and number_2) are amicable.
     Arguments must be positive integers.
     
     Examples:
@@ -55,10 +55,10 @@ def is_amicable_pair(a: int, b: int) -> bool:
     >>> is_amicable_pair(42, 42)
     False
     """
-    if a <= 0 or b <= 0:
+    if number_1 <= 0 or number_2 <= 0:
         raise ValueError("Numbers must be positive integers.")
-
-    return sum_of_divisors(a) == b and sum_of_divisors(b) == a
+    
+    return sum_of_divisors(number_1) == number_2 and sum_of_divisors(number_2) == number_1
 
 if __name__ == "__main__":
     import doctest

From 9779c1a623a84c5729bc568302c330047ad1d42c Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 10 Oct 2023 15:13:42 +0000
Subject: [PATCH 12/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/amicable_pair.py | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
index ac50168f7deb..a15a0a87dcf5 100644
--- a/maths/amicable_pair.py
+++ b/maths/amicable_pair.py
@@ -13,6 +13,7 @@
 to find the sum of the proper divisors of a number.
 """
 
+
 def sum_of_divisors(number: int) -> int:
     """
     Find the sum of the proper divisors of a number.
@@ -30,6 +31,7 @@ def sum_of_divisors(number: int) -> int:
 
     return sum
 
+
 def is_amicable_pair(number_1: int, number_2: int) -> bool:
     """
     Check if two numbers (number_1 and number_2) are amicable.
@@ -57,8 +59,11 @@ def is_amicable_pair(number_1: int, number_2: int) -> bool:
     """
     if number_1 <= 0 or number_2 <= 0:
         raise ValueError("Numbers must be positive integers.")
-    
-    return sum_of_divisors(number_1) == number_2 and sum_of_divisors(number_2) == number_1
+
+    return (
+        sum_of_divisors(number_1) == number_2 and sum_of_divisors(number_2) == number_1
+    )
+
 
 if __name__ == "__main__":
     import doctest

From aa4d4e8b89cecd6252dffe72b0b6d5850bea9d96 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 20:45:55 +0530
Subject: [PATCH 13/19] spacing

---
 maths/amicable_pair.py | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
index ac50168f7deb..c392671db352 100644
--- a/maths/amicable_pair.py
+++ b/maths/amicable_pair.py
@@ -2,7 +2,7 @@
 Amicable numbers are two different natural numbers such that the sum
 of the proper divisors of each is equal to the other number.
 That is, s(a)=b and s(b)=a, where s(n) is equal to
-the sum of positive divisors of n except n itself.
+the 'sum' of positive divisors of n except n itself.
 Here, a and b form a pair of amicable numbers.
 
 More information about amicable numbers can be found here:
@@ -10,7 +10,7 @@
 
 Here, we have defined a function to check if two numbers are amicable.
 We have also defined an auxiliary function,
-to find the sum of the proper divisors of a number.
+to find the 'sum' of the proper divisors of a number.
 """
 
 def sum_of_divisors(number: int) -> int:
@@ -57,8 +57,11 @@ def is_amicable_pair(number_1: int, number_2: int) -> bool:
     """
     if number_1 <= 0 or number_2 <= 0:
         raise ValueError("Numbers must be positive integers.")
-    
-    return sum_of_divisors(number_1) == number_2 and sum_of_divisors(number_2) == number_1
+
+    if sum_of_divisors(number_1) == number_2 and sum_of_divisors(number_2) == number_1:
+        return True
+    else:
+        return False
 
 if __name__ == "__main__":
     import doctest

From 52c2cb82d7210d704229ea9ef2deeb45a397e267 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 10 Oct 2023 15:17:23 +0000
Subject: [PATCH 14/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/amicable_pair.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
index 0bc287d744da..ed8f9184353d 100644
--- a/maths/amicable_pair.py
+++ b/maths/amicable_pair.py
@@ -65,6 +65,7 @@ def is_amicable_pair(number_1: int, number_2: int) -> bool:
     else:
         return False
 
+
 if __name__ == "__main__":
     import doctest
 

From 643958b1f429bf9afdb7ebdab235a1fad183bf1f Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Tue, 10 Oct 2023 20:48:27 +0530
Subject: [PATCH 15/19] removed

---
 maths/amicable_pair.py | 71 ------------------------------------------
 1 file changed, 71 deletions(-)
 delete mode 100644 maths/amicable_pair.py

diff --git a/maths/amicable_pair.py b/maths/amicable_pair.py
deleted file mode 100644
index 0bc287d744da..000000000000
--- a/maths/amicable_pair.py
+++ /dev/null
@@ -1,71 +0,0 @@
-"""
-Amicable numbers are two different natural numbers such that the sum
-of the proper divisors of each is equal to the other number.
-That is, s(a)=b and s(b)=a, where s(n) is equal to
-the 'sum' of positive divisors of n except n itself.
-Here, a and b form a pair of amicable numbers.
-
-More information about amicable numbers can be found here:
-https://en.wikipedia.org/wiki/Amicable_numbers
-
-Here, we have defined a function to check if two numbers are amicable.
-We have also defined an auxiliary function,
-to find the 'sum' of the proper divisors of a number.
-"""
-
-
-def sum_of_divisors(number: int) -> int:
-    """
-    Find the sum of the proper divisors of a number.
-
-    Examples:
-    >>> sum_of_divisors(220)
-    284
-    >>> sum_of_divisors(284)
-    220
-    """
-    sum = 0
-    for i in range(1, number):
-        if number % i == 0:
-            sum += i
-
-    return sum
-
-
-def is_amicable_pair(number_1: int, number_2: int) -> bool:
-    """
-    Check if two numbers (number_1 and number_2) are amicable.
-    Arguments must be positive integers.
-
-    Examples:
-    >>> is_amicable_pair(220, 284)
-    True
-    >>> is_amicable_pair(1184, 1210)
-    True
-    >>> is_amicable_pair(127, 729)
-    False
-    >>> is_amicable_pair(7, 13)
-    False
-    >>> is_amicable_pair(0, 12)
-    Traceback (most recent call last):
-        ...
-    ValueError: Numbers must be positive integers.
-    >>> is_amicable_pair(12, -1)
-    Traceback (most recent call last):
-        ...
-    ValueError: Numbers must be positive integers.
-    >>> is_amicable_pair(42, 42)
-    False
-    """
-    if number_1 <= 0 or number_2 <= 0:
-        raise ValueError("Numbers must be positive integers.")
-
-    if sum_of_divisors(number_1) == number_2 and sum_of_divisors(number_2) == number_1:
-        return True
-    else:
-        return False
-
-if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()

From c05ed7cc8a6821315b477abb6161dd8e993d8a29 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Thu, 12 Oct 2023 21:54:51 +0530
Subject: [PATCH 16/19] changed name of file and added code improvements

---
 ...olecules.py => speeds_of_gas_molecules.py} | 38 +++++++++++++------
 1 file changed, 26 insertions(+), 12 deletions(-)
 rename physics/{avg_and_mps_speeds_of_gaseous_molecules.py => speeds_of_gas_molecules.py} (75%)

diff --git a/physics/avg_and_mps_speeds_of_gaseous_molecules.py b/physics/speeds_of_gas_molecules.py
similarity index 75%
rename from physics/avg_and_mps_speeds_of_gaseous_molecules.py
rename to physics/speeds_of_gas_molecules.py
index 3157741208e9..004670148530 100644
--- a/physics/avg_and_mps_speeds_of_gaseous_molecules.py
+++ b/physics/speeds_of_gas_molecules.py
@@ -46,10 +46,8 @@
 temperature and molar mass of the gas.
 """
 
-# necessary constants
-PI = 3.1415926535  # pi
-R = 8.3144626181  # gas constant
-
+# import the constants R and PI from the scipy.constants library
+from scipy.constants import R, pi as PI
 
 def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
@@ -58,16 +56,24 @@ def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
 
     Examples:
     >>> avg_speed_of_molecule(273, 0.028) # nitrogen at 273 K
-    454.34887551126405
+    454.3488755020387
     >>> avg_speed_of_molecule(300, 0.032) # oxygen at 300 K
-    445.5257273482451
+    445.52572733919885
+    >>> avg_speed_of_molecule(-273, 0.028) # invalid temperature
+    Traceback (most recent call last):
+        ...
+    Exception: Absolute temperature cannot be less than 0 K
+    >>> avg_speed_of_molecule(273, 0) # invalid molar mass
+    Traceback (most recent call last):
+        ...
+    Exception: Molar mass should be greater than 0 kg/mol
     """
+
     if temperature < 0:
         raise Exception("Absolute temperature cannot be less than 0 K")
     if molar_mass <= 0:
         raise Exception("Molar mass should be greater than 0 kg/mol")
-    else:
-        return (8 * R * temperature / (PI * molar_mass)) ** 0.5
+    return (8 * R * temperature / (PI * molar_mass)) ** 0.5
 
 
 def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
@@ -77,16 +83,24 @@ def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:
 
     Examples:
     >>> mps_speed_of_molecule(273, 0.028) # nitrogen at 273 K
-    402.6562070215111
+    402.65620701908966
     >>> mps_speed_of_molecule(300, 0.032) # oxygen at 300 K
-    394.83689555229637
+    394.836895549922
+    >>> mps_speed_of_molecule(-273, 0.028) # invalid temperature
+    Traceback (most recent call last):
+        ...
+    Exception: Absolute temperature cannot be less than 0 K
+    >>> mps_speed_of_molecule(273, 0) # invalid molar mass
+    Traceback (most recent call last):
+        ...
+    Exception: Molar mass should be greater than 0 kg/mol
     """
+
     if temperature < 0:
         raise Exception("Absolute temperature cannot be less than 0 K")
     if molar_mass <= 0:
         raise Exception("Molar mass should be greater than 0 kg/mol")
-    else:
-        return (2 * R * temperature / molar_mass) ** 0.5
+    return (2 * R * temperature / molar_mass) ** 0.5
 
 
 if __name__ == "__main__":

From 886fb5d37f6290c2c51d0db8846d38e4c2befe53 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 12 Oct 2023 16:25:28 +0000
Subject: [PATCH 17/19] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 physics/speeds_of_gas_molecules.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/physics/speeds_of_gas_molecules.py b/physics/speeds_of_gas_molecules.py
index 004670148530..18de1f466cc1 100644
--- a/physics/speeds_of_gas_molecules.py
+++ b/physics/speeds_of_gas_molecules.py
@@ -49,6 +49,7 @@
 # import the constants R and PI from the scipy.constants library
 from scipy.constants import R, pi as PI
 
+
 def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
     Takes the temperature (in K) and molar mass (in kg/mol) of a gas

From 97b89cdfdfe4024afcc29eeda08bdce268fffe28 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Thu, 12 Oct 2023 21:57:34 +0530
Subject: [PATCH 18/19] issues fixed due to pi

---
 physics/speeds_of_gas_molecules.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/physics/speeds_of_gas_molecules.py b/physics/speeds_of_gas_molecules.py
index 004670148530..c73201767001 100644
--- a/physics/speeds_of_gas_molecules.py
+++ b/physics/speeds_of_gas_molecules.py
@@ -46,8 +46,8 @@
 temperature and molar mass of the gas.
 """
 
-# import the constants R and PI from the scipy.constants library
-from scipy.constants import R, pi as PI
+# import the constants R and pi from the scipy.constants library
+from scipy.constants import R, pi
 
 def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
     """
@@ -73,7 +73,7 @@ def avg_speed_of_molecule(temperature: float, molar_mass: float) -> float:
         raise Exception("Absolute temperature cannot be less than 0 K")
     if molar_mass <= 0:
         raise Exception("Molar mass should be greater than 0 kg/mol")
-    return (8 * R * temperature / (PI * molar_mass)) ** 0.5
+    return (8 * R * temperature / (pi * molar_mass)) ** 0.5
 
 
 def mps_speed_of_molecule(temperature: float, molar_mass: float) -> float:

From 1c2b7b2e5f905a8257725cfe39806f87936e2594 Mon Sep 17 00:00:00 2001
From: Baron105 <barunparua@gmail.com>
Date: Thu, 12 Oct 2023 22:24:17 +0530
Subject: [PATCH 19/19] requested changes added

---
 physics/speeds_of_gas_molecules.py | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/physics/speeds_of_gas_molecules.py b/physics/speeds_of_gas_molecules.py
index 92cc607da9cd..a50d1c0f6d76 100644
--- a/physics/speeds_of_gas_molecules.py
+++ b/physics/speeds_of_gas_molecules.py
@@ -1,8 +1,9 @@
 """
-The root-mean-square, average and most probable speeds are derived from
-the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann distribution is a
-probability distribution that describes the distribution of speeds for particles
-in a gas.
+The root-mean-square, average and most probable speeds of gas molecules are
+derived from the Maxwell-Boltzmann distribution. The Maxwell-Boltzmann
+distribution is a probability distribution that describes the distribution of
+speeds of particles in an ideal gas.
+
 The distribution is given by the following equation:
 
         -------------------------------------------------
@@ -22,7 +23,7 @@
 from 0 to infinity and dividing by the total number of molecules. The result is:
 
         ---------------------
-        | vavg = √8RT/πM    |
+        | vavg = √(8RT/πM)  |
         ---------------------
 
 The most probable speed is the speed at which the Maxwell-Boltzmann distribution
@@ -30,7 +31,7 @@
 distribution with respect to v and setting the result equal to zero. The result is:
 
         ---------------------
-        | vmp = √2RT/M      |
+        | vmp = √(2RT/M)    |
         ---------------------
 
 The root-mean-square speed is another measure of the average speed
@@ -38,7 +39,7 @@
 of the average of the squares of the speeds of the molecules. The result is:
 
         ---------------------
-        | vrms = √3RT/m     |
+        | vrms = √(3RT/M)   |
         ---------------------
 
 Here we have defined functions to calculate the average and