Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\,K$ . the position of $A$ is free to move while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\,K$ , then the rise in temperature of the gas in $B$ is   .... $K$

Which of the following graphs correctly represents the variation of $\beta  =  - \left( {\frac{{dV}}{{dP}}} \right)/V$ with $P$ for an ideal gas at constant temperature ?

In an adiabatic expansion of a gas initial and final temperatures are ${T_1}$ and ${T_2}$ respectively, then the change in internal energy of the gas is

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

Six moles of an ideal gas performs a cycle shown in figure. If the temperatures are $T_A = 600\, K,$ $T_B = 800\,K,$ $T_C = 2200\,K$ and $T_D = 1200\,K,$ then the work done per cycle is approximately ...... $kJ$

An ideal heat engine operates on Carnot cycle between $227\,^oC$ and $127\,^oC$. It absorbs $6 \times 10^4\, cal$ at the higher temperature. The amount of heat converted into work equals to