A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac {1}{6}$ . When $T_2$ is lowered by $60\,K$ ; its efficiency increases to $\frac {1}{3}$. Then $T_1$ and $T_2$ are respectively

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

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 $1\rightarrow 2\,\,?$ …… $J$

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then

For free expansion of a gas, which is true