For an ideal heat engine,the temperature of the source is $127\,^{\circ} C$. In order to have $60\, \%$ efficiency,the temperature of the sink should be $........\,{ }^{\circ} C$. (Round off to the nearest integer)

$A$ 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 ....... $K$.

$A$ Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature $600 \text{ K}$. For the same sink temperature, to increase its efficiency to $80 \%$, the temperature of the source is (in $\text{ K}$)

An ideal gas heat engine operates in a Carnot cycle between $227^{\circ}C$ and $127^{\circ}C$. It absorbs $6 \times 10^4 \text{ cal}$ of heat at the higher temperature. The amount of heat converted to work is ......... $\times 10^4 \text{ cal}$.

Explain why the efficiency of a Carnot engine cannot be $100\%$?

$A$ 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 $K$)