The volume of a gas is reduced adiabatically to $(1/4)^{th}$ of its volume at $27\,^oC$ . If $\gamma = 1.4$ the new temperature is

A carnot engine, having an efficiency of $\eta  = 1/10$ as heat engine, is used as a refrigetator. If the work done on the system is $10\,J$ , the amount of energy absorbed from the reservoir at lower temperature is ………. $\mathrm{J}$

$P-V$ plots for two gases during adiabatic process are shown. Plots $(1)$ and $(2)$ corresponds to

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${C_p}/{C_v}$ for the gas 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 $1\rightarrow 2\,\,?$ …… $J$