Which of the following quantities does not characterize the thermodynamic state of a substance?

One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.

The relation between efficiency $(\eta)$ of a Carnot engine and the coefficient of performance $(\beta)$ of a refrigerator working between the same temperatures is:

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The process on the $P-V$ diagram is:

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4 V_1$. After this,the gas expands adiabatically and its volume becomes $32 V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{\text{iso}}$ and $W_{\text{adia}}$,respectively. If the ratio $\frac{W_{\text{iso}}}{W_{\text{adia}}} = f \ln 2$,then $f$ is:

The $VT$ curve for a thermodynamic process is given. Identify the corresponding $PV$ curve.