AP Physics 2 FRQ practice

On the dot shown in the force diagram, representing the piston, draw and label the forces that are exerted on the piston. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.

Derive an expression for the internal energy of the gas in terms of $M$, $A$, $V_0$, $P_{\text{atm}}$, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

On the axes provided in Figure 2, sketch the expected relationship between the pressure $P$ and volume $V$ of the gas for the thermodynamic process that the gas undergoes while the block is being added. Draw an arrow on your sketch to represent the direction of the thermodynamic process. A metal block of mass $m_b = 3.0\ \text{kg}$ is gently placed on top of the piston. The block is added slowly enough that the gas remains in thermal equilibrium with the reservoir at $T_0$ throughout the compression, and the piston comes to rest at a new equilibrium position.

Indicate whether the entropy change of the gas, $\Delta S_{\text{gas}}$, from the moment the reservoir is set to $T_{\text{new}}$ until the gas reaches equilibrium at $T_{\text{new}}$ is positive, negative, or zero. With the block still on the piston, the thermal reservoir is changed to a new constant temperature $T_{\text{new}} = 360\ \text{K}$. The gas is allowed to reach thermal equilibrium with the reservoir, and the piston comes to rest at a new final volume. The cylinder wall through which conduction occurs has thickness $L = 2.0× 10^{-3}\ \text{m}$, thermal conductivity $k = 15\ \text{W/(m}\cdot\text{K)}$, and contact area with the gas $A_w = 1.0× 10^{-2}\ \text{m}^2$. During the initial part of the heating, while the gas temperature is $T_g = 300\ \text{K}$ and the reservoir temperature is $T_{\text{new}} = 360\ \text{K}$, assume the temperature difference across the wall is approximately constant.