$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62\, K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are,respectively:

The efficiency of a Carnot engine when the source temperature is $T_1$ and the sink temperature is $T_2$ is given by:

$A$ Carnot heat engine works with an ideal diatomic gas and an adiabatic volume expansion ratio of $32$. Then its efficiency is ....... $\%$

In a Carnot engine,the temperature of the reservoir is $527^{\circ} C$ and that of the sink is $200 \; K$. If the work done by the engine when it transfers heat from the reservoir to the sink is $12000 \; kJ$,the quantity of heat absorbed by the engine from the reservoir is $x \times 10^{6} \; J$. Find the value of $x$.

$A$ Carnot engine absorbs an amount $Q$ of heat from a reservoir at an absolute temperature $T$ and rejects heat to a sink at a temperature of $T/3$. The amount of heat rejected is

$A$ Carnot heat engine has an efficiency of $50 \%$. The temperature of the sink is maintained at $500 \ K$. To increase the efficiency up to $80 \%$, the required increment in the source temperature is: (in $K$)