Two moles of a gas at a temperature of $327^{\circ} C$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$,then the work done by the gas is (Universal gas constant $= 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $kJ$)

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process,which of the following is true?

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27V$ is . . . . . . $J$.

The pressure and density of a diatomic gas with $\gamma = 7/5$ change adiabatically from $(P, d)$ to $(P', d').$ If $\frac{d'}{d} = 32,$ then $\frac{P'}{P}$ is

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ}C$ to $37^{\circ}C$. If the ideal gas is composed of polyatomic molecules that have $4$ vibrational modes,which of the following is true?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process,the change in internal energy of a gas is equal to the work done on/by the gas in the process.
Statement $2:$ The temperature of a gas remains constant in an adiabatic process.