$A$ 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

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 $K$)

$A$ reversible engine and an irreversible engine are working between the same temperatures. The efficiency of the ...........

In a Carnot engine,when the temperatures are $T_2 = 0^{\circ} C$ and $T_1 = 200^{\circ} C$,its efficiency is $\eta_1$. When the temperatures are $T_1 = 0^{\circ} C$ and $T_2 = -200^{\circ} C$,its efficiency is $\eta_2$. Then the value of $\frac{\eta_1}{\eta_2}$ is:

$A$ Carnot engine $(E)$ is working between two temperatures $473 \ K$ and $273 \ K$. In a new system,two engines are used: engine $E_1$ works between $473 \ K$ and $373 \ K$,and engine $E_2$ works between $373 \ K$ and $273 \ K$. If $\eta_{12}$,$\eta_1$,and $\eta_2$ are the efficiencies of the engines $E$,$E_1$,and $E_2$ respectively,then:

$A$ Carnot engine takes $300$ calories of heat from a source at $500 \,K$ and rejects $150$ calories of heat to the sink. The temperature of the sink is (in $\,K$)