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

Two Carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat $Q_1$ at temperature $T_1$ and rejects heat $Q$ to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ (i.e.,$Q/2$) and rejects heat $Q_3$ to the sink at temperature $T_3$. When the work done in both cases is equal,the value of $T$ is:

The work done by a Carnot engine operating between $300 \,K$ and $400 \,K$ is $400 \,J$. The energy exhausted by the engine is (in $\,J$)

An engine is supposed to operate between two reservoirs at temperatures $727^oC$ and $227^oC$. The maximum possible efficiency of such an engine is:

$A$ reversible Carnot heat engine converts $\frac{1}{4}$ of its input heat into work. When the temperature of the sink is reduced by $50 \ K$,its efficiency becomes $33 \frac{1}{3} \%$. The initial temperatures of the source and the sink respectively are

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$, the efficiency of the engine is doubled. The temperatures of the source and sink are