Physic Labs

Problem 2

One mole of monatomic ideal gas initially at T0=300 KT_0=300\,\mathrm K and volume V0=2.0 LV_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 2V02V_0. Assume quasistatic equilibrium, neglect piston friction, and use R=8.31 J/(mol K)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.
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ΔU=32R(Tf−T0)=32RT0=3.74×103 J\Delta U=\frac32R(T_f-T_0)=\frac32RT_0=3.74\times10^3\,\mathrm J
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The internal energy of an ideal gas depends only on temperature. For one mole of monatomic gas, CV=3R/2C_V=3R/2; a 300 K300\,\mathrm K rise therefore gives a positive change.