An ideal gas is expanding such that $PT^2$ = constant. The coefficient of volume expansion of the gas is :-

$P-V$ diagram of an ideal gas is as shown. Find work done by the gas in $ABCD$ process

A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficientcy $\frac{1}{6}$ . When $T_2$ is lowered by $62\,K$, its efficiency increases to $\frac{1}{3}$ . Then $T_1$ and $T_2$ are, respectively

Choose the incorrect statement from the following

$S1$: The efficiency of a heat engine can be $1$, but the coefficient of performance of a refrigerator can never be infinity

$S2$: The first law of thermodynamics is basically the principle of conservation of energy

$S3$: The second law of thermodynamics does not allow several phenomena consistent with the first law

$S4$: A process, whose sole result is the transfer of heat from a colder to a hotter object is impossible

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas, is

In a Carnot engine, the temperature of reservoir is $927\ ^oC$ and that of sink is $27\ ^oC.$ If the work done by the engine is $12.6 \times 10^6 J,$ the quantitiy of heat absorbed by the engine from the reservoir is