Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperatures in different states are: $T_1 = 400\, K, T_2 = 800\, K, T_3 = 2400\, K$ and $T_4 = 1200\, K.$ The work done by the gas during the cycle is ........ $kJ$.

Initial pressure and volume of a gas are $P$ and $V$ respectively. First,it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$. The final pressure of the gas will be

Which of the following statements is correct regarding the $p-V$ graph?
$1$. The slope of the $p-V$ graph in an isothermal process is $-\frac{p}{V}$.
$2$. The slope of the $p-V$ graph in an adiabatic process is $-\frac{p}{V}$.
$3$. The slope of the $p-V$ graph in an isochoric process is $-\frac{\gamma p}{V}$.
$4$. The slope of the $p-V$ graph in an isobaric process is zero.

Two identical vessels $A$ and $B$ contain equal amounts of an ideal monoatomic gas. The piston of $A$ is fixed,while the piston of $B$ is free to move. The same amount of heat $\Delta Q$ is absorbed by both $A$ and $B$. If the internal energy of $B$ increases by $100 \, J$,what is the change in the internal energy of $A$ (in $, J$)?

The $VT$ curve for a thermodynamic process is given. Identify the corresponding $PV$ curve.

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)