Thermal Physics Questions

A $p-v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The cycle is a rectangle with vertices $(v_0,p_0),(2v_0,p_0),(2v_0,2p_0),(v_0,2p_0)$. The amount of heat extracted from the source in a single cycle is:

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature ${\theta }_0$, the graph between the temperature $T$ of the metal and time $t$ will be closest to: