Helium at $27^oC$ has a volume of $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be ....... $^oC$ $[\gamma = 5/3]$

In a thermodynamic system,$\Delta U$ represents the increase in internal energy and $W$ represents the work done by the system. Which of the following statements is true?

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5 \ L$ to $4 \ L$. The ratio of initial pressure to final pressure 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?

For $1 \text{ mole}$ of an ideal gas,during an adiabatic process,the square of the pressure of a gas is found to be proportional to the cube of its absolute temperature. The specific heat of the gas at constant volume is ($R$ is universal gas constant)

During adiabatic expansion,if the temperature of $3$ moles of a diatomic gas decreases by $50^{\circ} C$,then the work done by the gas is (where $R$ is the Universal gas constant). (in $R$)