1.Problem: A gas is contained in a cylinder with a movable

piston. The initial volume of the gas is 2.5 L, the initial pressure

is 1 atm, and the initial temperature is 20 °C. The piston is

pushed in, reducing the volume to 1.5 L. What is the final

pressure of the gas?

Solution: Using the ideal gas law (PV = nRT), we can calculate the

final pressure of the gas by rearranging the equation to P = (nRT)/V. Since the number of moles of gas (n), the gas constant (R), and the

temperature (T) remain constant, we can say that P1V1 = P2V2.

Therefore, P2 = (P1V1)/V2 = (1 atm * 2.5 L) / 1.5 L = 2 atm.

2,Problem: A gas is heated from 20 °C to 40 °C at constant

volume. What is the final pressure of the gas?

Solution: Using the ideal gas law (PV = nRT), we can calculate the

final pressure of the gas by rearranging the equation to P = (nRT)/V.

Since the number of moles of gas (n) and the volume (V) remain

constant, we can say that P1/T1 = P2/T2. Therefore, P2 = P1 * (T2/

T1) = P1 * (40 + 273.15) / (20 + 273.15) = P1 * 1.33.

3. Problem: A gas is expanded isothermally (at constant

temperature) from an initial volume of 2 L to a final volume of 4

L. What is the work done by the gas?

Solution: Using the ideal gas law (PV = nRT), we can calculate the

work done by the gas by using the equation for work done in an

isothermal expansion: W = nRT * ln(V2/V1). Since the temperature

(T) remains constant, we can say that nRT = constant. Therefore, W

= (constant) * ln(4/2) = (constant) * ln(2) = (constant) .

Here is an example of a python function that calculates the final pressure of a gas in an isothermal expansion process:

```
import math
def isothermal_expansion(P1, V1, V2, T):
# P1 = initial pressure
# V1 = initial volume
# V2 = final volume
# T = temperature (in kelvin)
P2 = P1 * (V2/V1)
return P2
```

You can use this function to find the final pressure of a gas in an isothermal expansion process.

You can also use this function to find the final temperature in an adiabatic compression process:

```
def adiabatic_compression(P1, V1, V2, T1):
# P1 = initial pressure
# V1 = initial volume
# V2 = final volume
# T1 = initial temperature (in kelvin)
gamma = 5/3
T2 = P1*V1**(2/3)*T1 / V2**(2/3)
return T2
```

You can use this function to find the final temperature of a gas in an adiabatic compression process.

Keep in mind that these are examples and you may need to adjust them based on your specific use case.

Here is an example of a python function that calculates the work done by a gas in an isothermal expansion process:

```
import math
def isothermal_work(n, R, T, V1, V2):
# n = number of moles of gas
# R = gas constant
# T = temperature (in kelvin)
# V1 = initial volume
# V2 = final volume
W = n*R*T*math.log(V2/V1)
return W
```

You can use this function to find the work done by a gas in an isothermal expansion process.

And here is an example of a python function that calculates the final pressure of a gas in an adiabatic expansion process:

```
def adiabatic_expansion(P1, V1, V2):
# P1 = initial pressure
# V1 = initial volume
# V2 = final volume
gamma = 5/3
P2 = P1 * (V2/V1)**(3-gamma)
return P2
```

You can use this function to find the final pressure of a gas in an adiabatic expansion process.

It’s worth noting that these are examples and you may need to adjust them based on your specific use case and the specific gas you are working with. Additionally, these are based on the assumption that the gas is an ideal gas, if the gas is not ideal then the results will not be accurate.