🧲AP Physics 2
4. A rigid, sealed metal cylinder contains of a monatomic ideal gas. The cylinder is initially at thermal equilibrium with a large reservoir at temperature . The gas is then brought into thermal contact with a second large reservoir at a higher temperature , as shown in Figure 1. Heat flows through the metal wall into the gas until the gas reaches a new equilibrium temperature. During this heating, the volume of the gas remains constant because the cylinder is rigid. The pressure of the gas is monitored throughout the process.
Figure 1. A rigid, sealed cylinder of monatomic ideal gas (n = 0.80 mol) is heated at constant volume by contact with a higher-temperature reservoir (T2 = 450 K) after initially being in equilibrium with a reservoir at T1 = 300 K.
A student claims that when the gas is heated from to at constant volume, the pressure of the gas increases because the atoms move faster and collide with the walls more frequently and with greater momentum change per collision.
Indicate whether the student's claim is correct or incorrect. Without manipulating equations, justify your answer by referring to the motion of the gas atoms and how that motion affects the force exerted on the container walls.
Derive an expression for the change in internal energy of the gas during the heating process. Express your answer in terms of , , , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Indicate whether the expression you derived in part B is or is not consistent with your answer from part A. Briefly justify your answer by relating how a change in average atomic kinetic energy is connected to both internal energy and the observed pressure change at constant volume.
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