A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

The relation between efficiency $(\eta)$ of Carnot engine and coefficient of performance $\left(\eta_1\right)$ of refrigerator is

500 gram of a diatomic gas is enclosed at a pressure of $10^5 \mathrm{Nm}^{-2}$. The density of the gas is $5 \mathrm{kgm}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]

The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' $R$ ' from the centre of a star of radius ' $r$ ' is $(R>r)(\sigma=$ Stefan's constant $)$