The insulated cylinder shown in the diagram is closed at both ends and has a the

ID: 1432437 • Letter: T

Question

The insulated cylinder shown in the diagram is closed at both ends and has a thermally insulating piston

that is free to move on frictionless bearings. The piston divides the chamber into two compartments

containing gases A and B. Initially, each compartment has a volume of 5.0 x 10-2 m3 and contains a

monatomic ideal gas at a temperature of 0.0 °C and a pressure of 1.0 atm.

An amount of heat, Q, is now slowly (quasi-statically) added to gas A so that it expands, and therefore

gas B gets compressed. (The piston moves to the right.)

a) If the final pressure (after compression) of gas B is 3.0 atm, what is the final volume of gas B?

(Hint: Think about what it means for the piston to be thermally insulating.)

b) What are the final temperatures of the gases? (TAf = ?, TBf = ?)

c) How much heat was added to gas A? (Q = ?)

a) the final volume of gas B , V5/3 = 1 * (5.0 x 10-2 )5/3/3

=> V = 0.02589 m3

b) Final temperature of gas B

=> Tbf = 273.15 * 0.050.66/0.025890.66

= 421.75 K

Final temperature of gas A

=> Taf = 273.15 * 0.050.66/0.074110.66

= 210.67 K

c) heat was added to gas A = 0 J ( Adiabatic process)

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