In a Carnot engine,as the gas gives heat energy to the sink,the temperature of the sink

$A$ 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 $6\,kcal$ at the higher temperature. The amount of heat (in $kcal$) converted into work is equal to

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:

$A$ Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. How much heat in $kcal/s$ should it consume per second to deliver mechanical work at the rate of $1.0\,kW$?

What is the theoretical efficiency of a heat engine?