$A$ Carnot engine has an efficiency of $50 \%$. If the temperature of the sink is reduced by $40 \, K$,its efficiency increases by $30 \%$. The temperature of the source will be $.... \, K$.

$A$ Carnot engine has the same efficiency between $800 \ K$ and $500 \ K$ and between $x \ K$ and $600 \ K$. The value of '$x$' is: (in $K$)

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?

Two Carnot engines $A$ and $B$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $T$. The second engine $B$ receives the heat at temperature $T$ and rejects to its sink at temperature $T_2$. For what value of $T$ are the efficiencies of the two engines equal?

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

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.