The efficiency of an ideal Carnot engine working between temperatures $T_1$ and $T_2$ is $1/3$. If the temperature of the sink is reduced by $40 \%$,then its efficiency will be: (in $\%$)

The efficiency of a Carnot engine which operates between the two temperatures $T_{1} = 500 \ K$ and $T_{2} = 300 \ K$ is: (in $\%$)

$A$ Carnot engine is made to work between $200\,^{\circ}C$ and $0\,^{\circ}C$ first and then between $0\,^{\circ}C$ and $-200\,^{\circ}C$. The ratio of efficiencies $\left( \frac{\eta_2}{\eta_1} \right)$ of the engine in the two cases is:

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ An inventor claims to have constructed an engine that has an efficiency of $30\%$ when operated between the boiling and freezing points of water. This is not possible.
Statement $2:$ The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.

$A$ Carnot engine working between $300\, K$ and $600\, K$ has a work output of $800\, J$ per cycle. How much heat energy is supplied to the engine from the source in each cycle? .... $J$

Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.