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 ........ $kJ$.

In the $P-V$ diagram shown,the gas does $5 \, J$ of work in the isothermal process $ab$ and $4 \, J$ of work in the adiabatic process $bc$. What will be the change in internal energy of the gas in the straight path $c$ to $a$ (in $, J$)?

One mole of an ideal monoatomic gas undergoes the process $A \rightarrow B \rightarrow C \rightarrow D \rightarrow A$ as shown in the graph. The work done during the process is

If $R$ is the universal gas constant,the amount of heat needed to raise the temperature of $2$ moles of an ideal monoatomic gas from $273 \ K$ to $373 \ K$ when no work is done is equal to ...... $R$.

$A$ polyatomic gas at pressure $P$,having volume $V$ expands isothermally to a volume $3V$ and then adiabatically to a volume $24V$. The final pressure of the gas is (for a polyatomic gas,assume degrees of freedom $f = 6$,so $\gamma = 4/3$):

The initial pressure and volume of a gas are $P$ and $V$ respectively. First,the gas is expanded to a volume of $9V$ by an isothermal process,and then it is compressed to a volume of $V$ by an adiabatic process. What is its final pressure (in $P$)? (Ratio of specific heat at constant pressure to constant volume $\gamma = \frac{3}{2}$)