A monoatomic gas at pressure '$$\mathrm{P}$$', having volume '$$\mathrm{V}$$' expands isothermally to a volume '$$2 \mathrm{~V}$$' and then adiabatically to a volume '$$16 \mathrm{~V}$$'. The final pressure of the gas is (Take $$\gamma=5 / 3$$ )

A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$$ is its initial volume. The initial temperature of the gas is $$T_i$$ in Kelvin and the final temperature is '$$x T_i$$'. The value of '$$x$$' is

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is 'E' Now due to change in temperature of that body, it radiates maximum energy at wavelength $$\frac{2 \lambda}{3}$$. At that temperature emissive power is