An ideal heat engine exhausting heat at $77^{\circ}C$ is to have a $30\%$ efficiency. It must take heat at ...... $^{\circ}C$.

In a Carnot engine,the temperature of the reservoir is $527^{\circ} C$ and that of the sink is $200 \; K$. If the work done by the engine when it transfers heat from the reservoir to the sink is $12000 \; kJ$,the quantity of heat absorbed by the engine from the reservoir is $x \times 10^{6} \; J$. Find the value of $x$.

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:

Consider a Carnot cycle operating between $T_1 = 500\, K$ and $T_2 = 300\, K$ producing $1\, kJ$ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from $2:3$ to $3:4$,the efficiency of the engine changes by (in $\%$)

$A$ Carnot heat engine works with an ideal diatomic gas and an adiabatic volume expansion ratio of $32$. Then its efficiency is ....... $\%$