Question

23 mg of nitrogen gas, assumed to behave ideally, at a pressure of 88 torr and at 22^oC undergoes an adiabatic free expansion into a vacuum (Joule experiment) to a final pressure of 34 torr.

a) Is the process reversible? Why or why not?
b) What is the final temperature of the system? Why? [ answer should be 22^oC]
c) What is ∆S for the system?

Answer 1

(a) Is the process reversible?

No, an adiabatic free expansion into a vacuum is an irreversible process because gas doesn´t generate any work at filling the entire container, and it is not possible to come back to the initial state without applying changes in mechanical or thermic states that would generate a work on the system.

In the free expansion, gas slides through non equilibrium states, because there are no external pressures to calculate any work, and we can not calculate any of the thermodynamic properties when the process is being carried out: the changes do not happen in an uniform way.

(b) What is the final temperature of the system?

For ideal gases in an adiabatic free expansion, the changes in internal energy must be zero due to the known equation:

But heat (Q) is zero for an adiabatic process. And work is zero because the gas is not pulling against an external presure. Then:

We know that mass (m) and heat capacity (Cv) are not zero. So, the change in the temperature must be zero, it is to say:

(c) What is the ΔS for the system?

For ideal gases, we can calculate the change in entropy by using the equation:

For ideal gases:

Then, entropy can be calculated using:

Solving by integration:

The number of moles of gas are.

And we can apply:

Change in entropy will be: