Question

A cylinder that contains 7kg of CO2 with molar mass 44kg/kmol, occupying a volume of 0.025 m^3 at 1.1 bar, is compressed reversibly until the pressure is 230pa. Calculate final temperature, work done on CO2, heat supplied when the process is isothermal.

Answer 1

The carbon dioxide (like air, nitrogen, oxygen, hydrogen, noble gases) can be treated as an ideal gas, so, the temperature can be found from the ideal gas law:

$$T=\frac{P_1V_1}{nR}=2.08\text K.$$

The work done by gas is

$$W=P_1V_1\ln\frac{V_2}{V_1},\\\space\\ \frac{P_1V_1}{T}=\frac{P_2V_2}{T},\\\space\\ \frac{V_2}{V_1}=\frac{P_1}{P_2},\\\space\\ W=P_1V_1\ln\frac{P_1}{P_2}=16970\text{ J}.$$

Heat supplied:

$$Q=\Delta U+W,\\\space\\ \Delta U=0,\\\space\\ Q=W=16970\text{ J}.$$