$A$ Carnot engine,whose efficiency is $40\%$,takes in heat from a source maintained at a temperature of $500\ K$. It is desired to have an engine of efficiency $60\%$. Then,the intake temperature for the same exhaust (sink) temperature must be ....... $K$.

The $p-V$ diagram of a Carnot's engine is shown in the graph below. The engine uses $1$ mole of an ideal gas as the working substance. From the graph,the area enclosed by the $p-V$ diagram is equal to the net work done by the engine. Given that the heat supplied to the gas is $8000 \ J$,calculate the net work done by the engine. (Note: The efficiency of a Carnot engine is $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$) (in $J$)

An engine is supposed to operate between two reservoirs at temperatures $727^oC$ and $227^oC$. The maximum possible efficiency of such an engine is:

$A$ Carnot engine works between $27^{\circ} C$ and $127^{\circ} C$. Heat supplied by the source is $500 \ J$. The heat ejected to the sink is (in $J$):

$A$ scientist claims that the efficiency of their heat engine,which operates between a source temperature of $127^{\circ}C$ and a sink temperature of $27^{\circ}C$,is $26\%$. Then:

$A$ diatomic gas is used in a Carnot heat engine. If the efficiency of the given Carnot heat engine is $80\%$,then find the ratio of the initial volume to the final volume of the gas during adiabatic expansion.