$A$ Carnot engine with efficiency $50 \%$ takes heat from a source at $600 \ K$. To increase the efficiency to $70 \%$,keeping the temperature of the sink same,the new temperature of the source will be (in $K$)

$A$ Carnot engine uses an ideal monoatomic gas first and then an ideal diatomic gas. If the source and sink temperatures are $411^{\circ}C$ and $69^{\circ}C$ respectively,and the engine extracts $1000 \, J$ of heat in each cycle,then the area enclosed by the $PV$ diagram is ........ $J$.

$A$ Carnot engine whose heat sink is at $27^{\circ} C$ has an efficiency of $40 \%$. By how much should its source temperature be changed so as to increase its efficiency to $60 \% (in $K$)?$

The following figure shows a Carnot engine that works between temperatures $T_1=400 \text{ K}$ and $T_2=200 \text{ K}$ and drives a Carnot refrigerator that works between temperatures $T_3=350 \text{ K}$ and $T_4=250 \text{ K}$. The quantity $\frac{Q_3}{Q_1}$ will be

$A$ diatomic gas is used in a Carnot heat engine. If the efficiency of the given Carnot heat engine is $80\%$,then find the ratio of the initial volume to the final volume of the gas during adiabatic expansion.

$A$ Carnot engine having efficiency $\frac{1}{6}$ operates between the source temperature $T_H$ and the sink temperature $T_C$. Its efficiency increases to $\frac{1}{3}$ when $T_C$ is decreased by $64 \text{ K}$. The temperatures $T_H$ and $T_C$ are respectively: