$A$ Carnot engine takes $3 \times 10^6$ calories 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

Determine the efficiency of a Carnot cycle if,in the adiabatic expansion,the volume becomes $3$ times its initial value and $\gamma = 1.5$.

The Carnot cycle (reversible) of a gas represented by a Pressure-Volume $(P-V)$ curve is shown in the diagram. Consider the following statements:
$I.$ Area $ABCD =$ Work done by the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in the cycle $= 0$
Which of these are correct?

The value of efficiency $\eta$ for a heat engine may lie between

$A$ diatomic ideal gas is used as the working substance in a Carnot engine. During the adiabatic expansion process,if the volume of the gas increases from $V$ to $32V$,what is the efficiency of the engine?

$A$ 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