A laboratory room is not airtight, so the air inside always remains at a constant atmospheric pressure of 1.01 × 105 Pa. The volume of the room is constant at 150 m3. The air inside the room behaves as an ideal gas. Over the course of the day, the air temperature in the room increases from 283 K (10∘C10 ^\circ\text{C}10∘C) to 303 K (30∘C30 ^\circ\text{C}30∘C).
Show that the total internal energy of the air remaining in the room is the same at all temperatures. 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) and an explanation of the molecular motion in terms of kinetic theory.
56 exam-style questions on OCR A A Level Physics Thermal physics, covering Temperature, Solid, liquid and gas, Thermal properties of materials, and Ideal gases. Each one has a worked solution and a mark scheme showing where the marks go.