Free expansion of gas: diaphragm vs frictionless piston

[pyroknife]

Why is there no change in temperature in this case?



Consequently, what happens with temperature?

I am having problems with looking at this conceptually. I will try to take another crack at justifying case A. Since there's no heat transfer and work in case A, that means there's no change in internal temperature. For a perfect gas, internal temperature is only a function of temperature. Since there's no change in internal energy, there's no change in temperatre. Temperature and internal energy are directly correlated

 

[voko]

Since there's no change in internal energy, there's no change in temperatre. Temperature and internal energy are directly correlated

And what does that imply for case B?

 

[pyroknife]

And what does that imply for case B?

Oh I see. Internal energy and temp would also be directly correlated for case B because the gas is still an ideal gas. There's no heat but there's a work output thus change in internal energy is negative, which implies change in temperature is negative (a decrease in temp from initial to final)!

 

[voko]

Correct. And what does lower final temperature imply for final pressure?

 

[pyroknife]

Correct. And what does lower final temperature imply for final pressure?

Sweet. Hmmm, wouldn't we have to know the change in temperature to determine whether the final pressure increase or decrease?

I forgot to mention the final volume is 6 times the original volume.

Let me work this out mathematically.

The left portion (1) has a volume 5x the volume of the right. I have use "f" index to denote final state rather than (2).
For case A:
P1V1=P_f*V_f, V_f=1/5V1+V1=6/5*V1
=>P_f=5/6*P1 (Decrease in pressure for case A)For case B:
P1V1/T1=P_f*V_f/T_f => P_f=5/6*P1*T_f/T1. The ratio T_f/T1 is less <1, thus P_f for case B is less than P_f for case A.
Is there any way to obtain the T_f/T1 ratio though?

 

[voko]

It is generally bad when one symbol means more than one thing, as is the case with your symbols labeled with "f". Your conclusion is correct, however.

I do not think it is possible to obtain final temperature/pressure in case B without making additional assumptions on the process.