In a Carnot engine,the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink. The efficiency of the engine is (in $\%$)

When the temperature difference between the source and sink increases,the efficiency of the heat engine

The efficiency of a Carnot engine is $\eta$ when its hot and cold reservoirs are maintained at temperatures $T_1$ and $T_2$,respectively. To increase the efficiency to $1.5 \eta$,the increase in temperature $(\Delta T)$ of the hot reservoir,while keeping the cold reservoir constant at $T_2$,is

$A$ Carnot engine having an efficiency of $40\%$ takes heat from a source maintained at a temperature of $500 \ K$. If the efficiency is to be increased to $60\%$ while keeping the sink temperature constant,what should be the new source temperature in $K$?

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by $60\,K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are respectively:

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?