In the kinetic theory of gases, we derive the equation pV=13Nm(crms)2pV = \frac{1}{3}Nm(c_{\text{rms}})^2pV=31Nm(crms)2 under several simplifying assumptions. State two assumptions made in this derivation, other than that the particles are identical and in continuous, rapid, random motion.
Using Newton's laws of motion, explain how the microscopic collisions of gas molecules with the container walls result in a macroscopic force exerted on the walls.
A high-altitude weather balloon has a volume of 0.45 m30.45\text{ m}^30.45 m3 containing helium gas at a pressure of 75 kPa75\text{ kPa}75 kPa. The mean kinetic energy of the helium atoms is 4.2×10−21 J4.2 \times 10^{-21}\text{ J}4.2×10−21 J. Calculate the amount of helium gas in the balloon in moles.
A gas cylinder is tested under isothermal conditions. A graph is plotted showing how its pressure varies with volume for a fixed mass of gas at an absolute temperature TTT. Describe how the curve of pressure against volume at temperature 1.8T1.8T1.8T compares to the original curve plotted at temperature TTT.
A point on the original curve has coordinates (0.015 m3,240 kPa)(0.015\text{ m}^3, 240\text{ kPa})(0.015 m3,240 kPa). Calculate the pressure of the gas at this same volume of 0.015 m30.015\text{ m}^30.015 m3 when the temperature is raised to 1.8T1.8T1.8T.
