Consider a cyclic process $\mathrm{P}\to \mathrm{Q}\to \mathrm{R}\to \mathrm{P}$ for a system. Among the following, the combination of steps that can never lead to this cyclic process is

($\mathrm{p}$: pressure, $\mathrm{V}$: volume, $\mathrm{T}$: temperature, $\mathrm{H}$: enthalpy, $\mathrm{S}$: entropy)

Among the following the number of state variable is

Internal energy $\left(\mathrm{U}\right)$

Volume $\left(\mathrm{V}\right)$

Heat $\left(\mathrm{q}\right)$

Enthalpy $\left(\mathrm{H}\right)$

Observe the following properties:

Volume, enthalpy, density, temperature, heat capacity, pressure, internal energy.

The number of extensive properties in the above list is

The total number of intensive properties from the following is _____.
Volume, Molar heat capacity, molarity, ${\mathrm{E}}_{\mathrm{cell}}^{\mathrm{o}}$,Gibbs free energy change, Molar mass, Mole

One mole of an ideal monoatomic gas undergoes two reversible processes $(\mathrm{A}\to \mathrm{B}$ and $\mathrm{B}\to \mathrm{C})$ as shown in the given figure:

$\mathrm{A}\to \mathrm{B}$ is an adiabatic process. If the total heat absorbed in the entire process $(\mathrm{A}\to \mathrm{B}$ and $\mathrm{B}\to \mathrm{C})$ is ${\mathrm{RT}}_2\ln 10$, the value of $2{\mathrm{logV}}_3$ is
[Use molar heat capacity of the gas at constant pressure, ${\mathrm{C}}_{\mathrm{p},\mathrm{m}}=\frac{5}{2}\mathrm{R}$]