$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^{\circ}C$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mol\cdot K)$

An ideal gas with constant heat capacity $C_V = \frac{3}{2} n R$ is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle.

$A$ monatomic gas of volume $V$ and pressure $P$ expands isothermally to a volume $27 V$ and then is compressed adiabatically to a volume $V$. The final pressure of the gas is: (in $P$)

The initial pressure and volume of a gas are $P$ and $V$ respectively. First, it is expanded isothermally to a volume $4V$ and then compressed adiabatically to a volume $V$. The final pressure of the gas will be (given $\gamma = 3/2$): (in $P$)

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \ K$. The piston 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 ..... $K$.