Problem 2

One mole of a monatomic ideal gas starts at

(P_0,V_0,T_0)

. It is heated at constant pressure until its volume is

2V_0

, then cooled at constant volume back to temperature

T_0

. Find the work done by the gas, the heat received by it over the full process, and its change in internal energy. Heat entering the gas is positive. Treat the gas as a closed system, apply the equation of state at each state, and use the stated sign convention to distinguish work from heat. (a) Relate temperature to volume on the first leg and specify pressure and volume at the junction. (b) Find the work on each leg and the total change in internal energy. (c) Use the first law to find net heat and explain why its sign need not match the heat on the cooling leg.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

P_0V_0=RT_0,\qquad T_1=\frac{P_0(2V_0)}{R}=2T_0

problems.proof.analysis

For one mole of ideal gas, $PV=RT$ . The pressure stays fixed while the volume doubles, so the temperature doubles as well.