$A$ Carnot engine has the same efficiency between $(i)$ $100 \ K$ and $600 \ K$ and (ii) $T \ K$ and $960 \ K$. The temperature $T$ in kelvin of the sink is

$A$ Carnot engine whose low temperature reservoir is at $7\,^{\circ}C$ has an efficiency of $50\%$. It is desired to increase the efficiency to $70\%$. By how many degrees should the temperature of the high temperature reservoir be increased? (in $K$)

$A$ car engine has a power of $20 kW$. The car makes a round trip of $1$ hour. If the thermal efficiency of the engine is $40 \%$ and the ambient temperature is $300 K$, the energy generated by fuel combustion is: (in $kJ$)

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

An engine operating between temperatures $T_1$ and $T_2$ has efficiency $\eta = \frac{1}{5}$. When $T_2$ is lowered by $45 \ K$,its efficiency becomes $\eta' = \frac{1}{2}$. Temperatures $T_1$ and $T_2$ are respectively:

The efficiency of an ideal heat engine working between the freezing point and boiling point of water is ........ $\%$