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

One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $8.0 \, m^{3}$ to $1.0 \, m^{3}$.
Step $2$: Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \, m^{3}$.
Step $3$: Then expanded adiabatically to volume $80.0 \, m^{3}$.
Step $4$: Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \, m^{3}$.
Then,$T_{1} / T_{2}$ is:

An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it, $2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ($R$ - universal gas constant).

What is the specific heat of a gas in an isothermal process and an adiabatic process?

$A$ gas expands with temperature according to the relation,$V=k T^{2/3}$,where $k$ is a constant. Work done when the temperature changes by $60 \ K$ is ($R=$ universal gas constant.) (in $R$)

An ideal gas with adiabatic exponent $(\gamma = 1.5)$ undergoes a process in which the work done by the gas is equal to the increase in the internal energy of the gas. The molar heat capacity of the gas for this process is: