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

State Carnot's theorem.

$A$ heat engine operates between a cold reservoir at temperature $T_{2} = 400 \, K$ and a hot reservoir at temperature $T_{1}$. It takes $300 \, J$ of heat from the hot reservoir and delivers $240 \, J$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be $.... K$.

Three designs are proposed for an engine which is to operate between $500 \ K$ and $300 \ K$. Design $A$ claims to produce $150 \ J$ of work per $1000 \ J$ of heat input, design $B$ $450 \ J$ of work per $1000 \ J$, and design $C$ $300 \ J$ of work per $1000 \ J$. Which of the designs would you choose?

For which of the following options will the efficiency of a Carnot engine be the highest?

$A$ Carnot engine whose efficiency is $40\%$ takes in heat from a source maintained at a temperature of $500 \ K$. It is desired to have an engine of efficiency $60\%$. Then,the intake temperature for the same exhaust (sink) temperature must be (in $K$)