$A$ 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 $K$)?$

$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.

The efficiency of a Carnot engine is $\eta$ when its hot and cold reservoirs are maintained at temperatures $T_1$ and $T_2$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir, while keeping the cold reservoir constant at $T_2$, is

$A$ car engine has a power of $20 kW$. The car makes a round trip of $1$ hour. If the thermal efficiency of the engine is $40 \%$ and the ambient temperature is $300 K$, the energy generated by fuel combustion is: (in $kJ$)

An ideal Carnot engine,whose efficiency is $40 \%$ receives heat at $500 \; K$. If its efficiency is $50 \%$ then the intake temperature for the same exhaust temperature is ......... $K$.