Spring 2006 7 Sm

A horizontal insulated cylinder is partitioned by a frictionless, insulating piston (which prevents heat exchange between the two sides). On each side of the piston, we have 30 liters of an ideal monatomic gas (CV = 3/2 nR and γ = 5/3 ) at a pressure of 1 atmosphere and a temperature T = 300 K. Heat is slowly injected into the gas on the left, causing the piston to move until the gas on the right is compressed to a pressure of P = 2 atmospheres.

(a) What are the final volume V and temperature T on the right side?

(b) What are the final values of P , V , and T on the left side?

(c) What is the change in the internal energy ∆U for the gas on the right side? How much heat Qif did it absorb, and how much work Wif is done to the right chamber?

(d.) What are the values of ∆U , Wif , and Qif for the gas on the left side?

Hint #1: For an ideal gas with adiabatic changes, P Vγ is constant.

Hint #2: The internal energy of an ideal gas is a function of temperature only.

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