At S.T.P., the mean free path of gas molecule is 1500 d , where ' $d$ ' is diameter of molecule. What will be the mean free path at 373 K at constant volume?

One mole of an ideal gas at an initial temperature of ' $T$ ' $K$ does ' $6 R$ ' of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5 / 3$, the final temperature of gas will be $\left(\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mole}^{-1} \mathrm{~K}^{-1}\right)$

The frequency ' $v_{\mathrm{m}}$ ' corresponding to which the energy emitted by a black body is maximum may vary with the temperature ' $T$ ' of the body as shown by the curves ' A ', ' B ', ' C ' and ' D ' in the figure. Which one of these represents the correct variation?

A metal rod cools at the rate of $$4{ }^{\circ} \mathrm{C} / \mathrm{min}$$ whon its temperature is $$90^{\circ} \mathrm{C}$$ and the rate of $$1{ }^{\circ} \mathrm{C} / \mathrm{m}{\text {in }}$$ when its temperature is $$30^{\circ} \mathrm{C}$$. The temperature of the surrounding is