One gram mole of a diatomic gas $(\gamma = 1.4)$ is compressed adiabatically so that its temperature rises from $27^{\circ}C$ to $127^{\circ}C$. The work done will be:

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

For an adiabatic expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to

When $2 \text{ moles}$ of a monatomic gas expands adiabatically from a temperature of $80^{\circ} C$ to $50^{\circ} C$,the work done is $W$. The work done when $3 \text{ moles}$ of a diatomic gas expands adiabatically from $50^{\circ} C$ to $20^{\circ} C$ is: (in $W$)

Identify the characteristics of an adiabatic process in a monoatomic gas.
$(A)$ Internal energy is constant.
$(B)$ Work done in the process is equal to the change in internal energy (in magnitude).
$(C)$ The product of temperature and volume is a constant.
$(D)$ The product of pressure and volume is a constant.
$(E)$ The work done to change the temperature from $T_1$ to $T_2$ is proportional to $(T_2 - T_1)$.
Choose the correct answer from the options given below.

By what factor should the volume of an ideal gas $(\gamma = 1.5)$ be increased through an adiabatic expansion so that its $rms$ speed becomes half?