$A$ Carnot engine takes $6000 \,cal$ of heat from a reservoir at $627^{\circ} C$ and gives it to a sink at $27^{\circ} C$. The work done by the engine is ......... $kcal$.

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.

Explain heat engines and their working.

$A$ Carnot engine $A$ working between temperatures $600 \ K$ and $T$ $(T < 600 \ K)$ and another Carnot engine $B$ working between temperatures $T$ $(T > 400 \ K)$ and $400 \ K$ are connected in series. If the work done by both the engines is the same, then $T =$ (in $K$)

$A$ Carnot engine working between $400\, K$ and $800\, K$ has a work output of $1200\, J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is ........... $J$

$A$ Carnot engine takes $300$ calories of heat from a source at $500 \,K$ and rejects $150$ calories of heat to the sink. The temperature of the sink is (in $\,K$)