$A$ diatomic ideal gas is used in a Carnot engine as the working substance. During the adiabatic expansion of the cycle,if the volume of the gas increases from $V$ to $32 V$,then the efficiency of the engine is

The ratio of the efficiencies of two Carnot engines $A$ and $B$ is $1.25$. The temperature difference between the source and the sink is the same in both engines. The ratio of the absolute temperatures of the sources of engines $A$ and $B$ is

$A$ Carnot engine operates between $627^{\circ}C$ and $227^{\circ}C$. The efficiency of the Carnot engine is ....... $\%$

The efficiency of a Carnot engine is $25 \%$,when the temperature of the sink is $300 \ K$. The increase in the temperature of the source required for the efficiency to become $50 \%$ is (in $K$)

$A$ Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is lowered by $57 \ K$,its efficiency becomes $\frac{1}{3}$. The temperature of the source is: (in $K$)

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