$A$ 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:

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 $K$)

Consider a two-stage Carnot engine. In the first stage,heat $Q_1$ is absorbed at temperature $T$ and heat $Q_2$ is expelled at temperature $\alpha T$ (where $\alpha < 1$). In the second stage,heat $Q_2$ is absorbed at temperature $\alpha T$ and heat $Q_3$ is expelled at temperature $\beta T$ (where $\beta < \alpha$). The efficiency of the Carnot engine will be

State Carnot's theorem.

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^\circ C$,the efficiency of the engine is doubled. The temperatures of the source and sink are:

The following figure shows a Carnot engine that works between temperatures $T_1=400 \text{ K}$ and $T_2=200 \text{ K}$ and drives a Carnot refrigerator that works between temperatures $T_3=350 \text{ K}$ and $T_4=250 \text{ K}$. The quantity $\frac{Q_3}{Q_1}$ will be