An experimental Martian habitat simulator is fitted with an automatic venting valve that maintains the internal gas pressure at a constant value of 7.80 × 104 Pa. The rigid chamber of the simulator has a constant volume of 140 m3. The gas inside behaves as an ideal gas. During a simulation run, the temperature of the gas is increased from 220 K to 290 K.
Show that the total internal energy of the gas remaining inside the simulator is independent of temperature. Support your answer with a calculations-based proof (assuming a monatomic ideal gas where internal energy U=32NkT\displaystyle U = \frac{3}{2}NkTU=23NkT), calculate this constant energy value, and explain this result in terms of the kinetic theory of gases.
