Problem 2

One mole of monatomic ideal gas initially at

T_0=300\,\mathrm K

and volume

V_0=2.0\,\mathrm L

is heated in a cylinder with a freely moving piston, so the gas pressure remains constant throughout. The gas expands to

2V_0

. Assume quasistatic equilibrium, neglect piston friction, and use

R=8.31\,\mathrm{J/(mol\,K)}

. (a) Find the final temperature and gas pressure. (b) Calculate the work done by the gas and its change in internal energy. (c) Find the heat transferred to the gas and state its sign.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{T_f=600\,\mathrm K,\ p_f=1.25\,\mathrm{MPa},\ W=2.49\,\mathrm{kJ},\ \Delta U=3.74\,\mathrm{kJ},\ Q=6.23\,\mathrm{kJ}}

problems.proof.analysis

The first-law check gives $Q-W=3.74\,\mathrm{kJ}=\Delta U$ . The signs agree with a gas that expands and warms.