$2$ moles of a diatomic gas undergoes the process : $PT_2/V$ = constant. Then, the molar heat capacity of the gas during the process will be equal to

A monoatomic ideal gas, initially at temperature $T_{1}$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature ${T}_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be

An ieal heat engine operates on Carnot cycle between $227\,^oC$ and $127\,^oC$. It absorbs $6 \times 10^4\, cal$ at the higher temperature. The amount of heat converted into work equals to

The efficiency of reversible engine is the irreversible engine.

If $R =$ universal gas constant, the amount of heat needed to raise the temperature of $2\, mol$ of an ideal monoatomic gas from $273\, K$ to $373\, K$ when no work is done is

Three processes compose a thermodynamics cycle shown in the $PV$ diagram. Process $1\rightarrow 2$ takes place at constant temperature. Process $2\rightarrow 3$ takes place at constant volume, and process $3\rightarrow 1$ is adiabatic. During the complete cycle, the total amount of work done is $10\,\, J$. During process $2\rightarrow 3$, the internal energy decrease by $20\,\,J$ and during process $3\rightarrow 1,$ $20\,\, J$ of work is done on the system. How much heat is added to the system during process $1\rightarrow 2\,\,?$ ...... $J$