A thermally insulated vessel contains a heat-insulating piston that moves without friction. Initially the piston is at the extreme left end and is joined to the right wall by a spring whose length equ

Question

A thermally insulated vessel contains a heat-insulating piston that moves without friction. Initially the piston is at the extreme left end and is joined to the right wall by a spring whose length equals the length of the cylinder. The right portion is evacuated and one mole of an ideal monoatomic gas is introduced in the left portion. Find the heat capacity of this spring-controlled monoatomic gas system, neglecting the heat capacities of the vessel, piston and spring.

TestHub · Accepted Answer

For displacement x the gas pressure balances the spring: P A = k x , so P V = k x 2 = RT . Work on the spring k x d x = d ( 2 k x 2 ​ ) = 2 R ​ d T . d Q = 2 3 ​ R d T + 2 R ​ d T = 2 R d T . C = 2 R .

Physics - Heat & Thermo Question with Solution | TestHub

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