$A$ Carnot engine with its cold body at $17\,^{\circ}C$ has $50\%$ efficiency. If the temperature of its hot body is now increased by $145\,^{\circ}C$,the efficiency becomes...... $\%$

$A$ Carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_1$ and $T_2$, where $T_1 > T_2$. If only $T_1$ is changed by $0.4 \%$, the change in efficiency is $\Delta \eta_1$, whereas if only $T_2$ is changed by $0.2 \%$, the efficiency is changed by $\Delta \eta_2$. The ratio $\frac{\Delta \eta_1}{\Delta \eta_2}$ is approximately,

An ideal Carnot engine whose efficiency is $50 \%$ receives heat at $500 \ K$. If the efficiency is to be $60 \%$, then the intake temperature for the same exhaust temperature is: (in $K$)

$A$ Carnot's engine operates with a source at $127^{\circ} C$ and a sink at $27^{\circ} C$. If the source supplies $40 \ kJ$ of heat energy,the work done by the engine is (in $kJ$)

$A$ Carnot engine, whose efficiency is $40\%$, takes heat from a source maintained at temperature $600\text{ K}$. To have an efficiency of $60\%$, the intake temperature for the same exhaust temperature should be: (in $\text{ K}$)

$A$ Carnot heat engine absorbs $600 \ J$ of heat from a source at a temperature of $127^{\circ} C$ and rejects $400 \ J$ of heat to a sink in each cycle. The temperature of the sink is (in $K$)