# Kinetic Theory of Gases

Problem (COP-Vol2-Ch24-Pr32): A container of volume 50 cc contains air (mean molecular weight = 28.8 g) and open to atmosphere where the pressure is 100 kPa. The container is kept in a bath containing melting ice ($0^{o}\mathrm{C}$). (a) Find the mass of the air in the container when thermal equilibrium is reached. (b) The container is now placed in another bath containing boiling water ($100^{o}\mathrm{C}$). Find the mass of air in the container. (c) The container is now closed and placed in the melting-ice bath. Find the pressure of the air when thermal equilibrium is reached.

Solution: The volume of the container is $V=50\times10^{-6}\,\mathrm{m^3}$, the atmospheric pressure pressure is $p=10^5\;\mathrm{Pa}$, and molecular weight of air is $M=28.8\;\mathrm{g}$. In case (a), temperature is $T=273\;\mathrm{K}$ and in case (b) temperature is $T=373\;\mathrm{K}$. Apply the ideal gas equation, $pV=nRT=\frac{m}{M}RT$ to get $m=0.0635\;\mathrm{g}$ in case (a) and $m=0.0464\;\mathrm{g}$ in case (b). In case (c), mass is $m=0.0464\;\mathrm{g}$ and temperature is $T=273\;\mathrm{K}$. Apply the ideal gas equation to get $p=\frac{mRT}{MV}=73\;\mathrm{kPa}$.