$A$ Carnot engine,whose efficiency is $40 \%$,takes heat from a source maintained at a temperature of $600 \ K$. If it is desired to have an efficiency of $60 \%$,then the intake temperature for the same exhaust (sink) temperature should be: (in $K$)

An engine performs $2000 \,J$ of mechanical work and discards $4000 \,J$ of heat each cycle. What is the thermal efficiency of the engine (in $\%$)?

An ideal heat engine exhausts heat at $77\,^{\circ}C$. To have a $30\%$ efficiency,it must take heat at what temperature in $^{\circ}C$?

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\,K$. If the temperature of the source is kept constant and its efficiency is to be raised to $60\%$,then the required temperature of the sink will be ........... $K$.

In the $1^{\text{st}}$ case,a Carnot engine operates between temperatures $300 \, K$ and $100 \, K$. In the $2^{\text{nd}}$ case,as shown in the figure,a combination of two engines is used. The efficiency of this combination (in the $2^{\text{nd}}$ case) will be:

$A$ 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,