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## Main Question or Discussion Point

Consider the following problem:

Gaseous helium (assumed ideal) filled in a horizontal cylindrical vessel is separated from its surroundings by a massless piston. Both piston and cylinder are thermally insulating. The ambient pressure is suddenly tripled without changing the ambient temperature. How many times of its initial value will the volume of the helium become, when the piston finally stops?

Initial pressure and volume be P1 and V1. Now the ambient pressure is

If I use the expression for adiabatic process i.e [tex] PV^\gamma =constant [/tex], then I don't get the answer at the back.

However, I can use 1st law to write[tex] W=-P_2\Delta V=3/2 nR\Delta T=3/2\Delta (PV)=3/2(P_2V_2-P_1V_1) [/tex] to get the correct answer.

I think the second way is fine. But why doesn't the first method work?

Gaseous helium (assumed ideal) filled in a horizontal cylindrical vessel is separated from its surroundings by a massless piston. Both piston and cylinder are thermally insulating. The ambient pressure is suddenly tripled without changing the ambient temperature. How many times of its initial value will the volume of the helium become, when the piston finally stops?

Initial pressure and volume be P1 and V1. Now the ambient pressure is

*suddenly*made P2 = 3 P1. The gas compresses under constant pressure P2, so the process must be isobaric. However the walls are also thermally insulating, so the process must also be Adiabatic. I find this confusing.If I use the expression for adiabatic process i.e [tex] PV^\gamma =constant [/tex], then I don't get the answer at the back.

However, I can use 1st law to write[tex] W=-P_2\Delta V=3/2 nR\Delta T=3/2\Delta (PV)=3/2(P_2V_2-P_1V_1) [/tex] to get the correct answer.

I think the second way is fine. But why doesn't the first method work?