$A$ Carnot engine takes $3 \times 10^6 \, \text{cal}$ 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:

Two Carnot engines $A$ and $B$ are operated in series. Engine $A$ receives heat from a reservoir at $600\,K$ and rejects heat to a reservoir at temperature $T$. Engine $B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at $100\,K$. If the efficiencies of the two engines $A$ and $B$ are equal,what is the value of the intermediate temperature $T$ and the ratio of their efficiencies $\frac{\eta_A}{\eta_B}$?

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

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

The efficiency of a Carnot engine is $50 \%$ when the temperature of the sink is $500 \ K$. If the efficiency of the Carnot engine is to be increased to $60 \%$,what should be the temperature of the sink,keeping the temperature of the source constant (in $K$)?

Explain: Carnot cycle and Carnot engine.