Me again (ideal gas/free expansion) soon

[don_anon25]

Here's my problem:
An ideal gas is allowed to expand freely into an evacuated chamber.
The gas is at a pressure of 5 bar and a temperature of 45 degrees Celsius.
Find the final temperature and pressure of the gas.
Find the entropy produced.

W=0, Q=0, dU=0, and dT=0. So the final temp. is 45 degrees Celsius.
I need pressure at final state though...
dU=0 implies that u1=u2. But I don't know what the gas is, so I can't get values for these.

Am I missing something obvious?

Please help soon!
Thanks!

 

[member 553083]

Since the gas is allowed to expand freely into an evacuated chamber, the final pressure of the gas will be equal to the atmospheric pressure. Therefore, the final pressure of the gas will be 1 bar. The entropy produced in this process can be calculated using the equation ∆S = ∆Q/T, where ∆Q is the heat transfer and T is the temperature of the system. Since no heat transfer occurs in this process, the entropy produced is 0.

 

[wais]

Hi there! It seems like you have the right idea so far. Since this is a free expansion, there is no work being done (W=0) and no heat being transferred (Q=0). This means that the change in internal energy (dU) is also 0.

You are correct that this implies that the initial internal energy (u1) is equal to the final internal energy (u2). However, since we don't know the specific gas being used, we can't determine the values for u1 and u2.

But, we can still find the final pressure and temperature using the ideal gas law: PV = nRT. Since the gas is expanding freely, the volume (V) increases while the number of moles (n) and the gas constant (R) remain constant. This means that the pressure (P) and temperature (T) must also change to maintain the equation.

To find the final pressure, we can use the initial pressure (5 bar) and volume (unknown) to solve for the final pressure. Similarly, we can use the initial temperature (45 degrees Celsius) and volume (unknown) to solve for the final temperature.

As for the entropy produced, we can use the equation ΔS = nRln(V2/V1) to calculate it. Again, since the number of moles and gas constant remain constant, we can use the initial and final volumes to find the change in entropy.

I hope this helps! Let me know if you have any other questions. Good luck!