Three separate reversible processes $\left(1,2 \mathrm{and} 3\right)$ are carried out with $1$ mole of an ideal gas initially at STP. In these processes, the pressure ($\mathrm{P}$) is measured while increasing any one of the quantities volume ($\mathrm{V}$), temperature ($\mathrm{T}$) and number of moles $\left(\mathrm{n}\right)$, keeping the other two constant. Plots of $\mathrm{P}\left(\mathrm{atm}\right)$ versus $\mathrm{X}$ are found to be linear, where $\mathrm{X}=\mathrm{n}$ or $\mathrm{T}\left(\mathrm{K}\right)$ or $1/\mathrm{V} \left({\mathrm{lit}}^{-1}\right)$. For the processes $1,2$ and $3$, the numerical values of the slopes ${\mathrm{m}}_1,{\mathrm{m}}_2$ and ${\mathrm{m}}_3$ of the $\mathrm{P}$ versus $\mathrm{X}$ plots are found to follow the order ${\mathrm{m}}_1>{\mathrm{m}}_2>{\mathrm{m}}_3$, respectively. The correct statement(s) about these processes is/are

($\mathrm{p}$: 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, ${\mathrm{C}}_{\mathrm{p},\mathrm{m}}=\frac{5}{2}\mathrm{R}$]