The rms speed of oxygen molecule in a gas is $u$, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be

The equation of state for 2 g of oxygen at a pressure ' $P$ ' and temperature ' $T$, when occupying a volume ' $V$ ' will be

The maximum wavelength of radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$, Wien's constant, $b=2898 \mu \mathrm{mK}$ )

If ' $C_P$ ' and ' $C_V$ ' are molar specific heats of an ideal gas at constant pressure and volume respectively. If ' $\lambda$ ' is the ratio of two specific heats and ' $R$ ' is universal gas constant then ' $C_p$ ' is equal to