Given below are two statements: Statement I: For an ideal gas, heat...

For an ideal gas, the relationship between heat capacity at constant pressure ($C_p$) and heat capacity at constant volume ($C_v$) is given by Mayer's relation:

$C_p - C_v = R$

Since the universal gas constant $R$ is a positive value, $C_p > C_v$. Thus, Statement I is false.

In a constant volume (isochoric) process, the change in volume $\Delta V = 0$.

Work done, $W = P\Delta V = 0$.

According to the first law of thermodynamics:

$\Delta U = q + W$

Since $W = 0$, we get $\Delta U = q_v$.

This means that in a constant volume process, no work is produced and all the heat absorbed by the system (withdrawn from the surroundings) goes entirely into increasing the internal energy (chaotic motion of the molecules). This increase in internal energy is reflected by an increase in the temperature of the ideal gas. Thus, Statement II is true.

Therefore, Statement I is false but Statement II is true.

Answer: Statement I is false but Statement II is true