In an adiabatic process for an ideal gas, the relation between the universal gas constant ' $R$ ' and specific heat at constant volume ' $\mathrm{C}_{\mathrm{v}}$ ' is $R=0.4 C_v$. The pressure ' $P$ ' of the gas is proportional to the temperature ' $T$ ', of the gas as $T^k$. The value of constant ' K ' is

The black discs $\mathrm{x}, \mathrm{y}$ and z have radii $1 \mathrm{~m}, 2 \mathrm{~m}$ and 3 m respectively. The wavelengths corresponding to maximum intensity are $200 \mathrm{~nm}, 300 \mathrm{~nm}$ and 400 nm respectively. The relation between emissive power $E_x, E_y$ and $E_z$ is

For a gas, $\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0.4$ where R is the universal gas constant and ' $\mathrm{C}_{\mathrm{V}}$ ' is molar specific heat at constant volume. The gas is made up of molecules which are

In a thermodynamic system ' $\Delta \mathrm{U}$ ' represents the increase in internal energy and ' $W$ ' the work done by the system. Which of the following statement is true?