The difference in length between two rods $$\mathrm{A}$$ and $$\mathrm{B}$$ is $$60 \mathrm{~cm}$$ at all temperatures. If $$\alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$$ and $$\beta_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$$, the lengths of the two rods are

An ideal gas expands adiabatically. $$(\gamma=1 \cdot 5)$$ To reduce the r.m.s. velocity of the molecules 3 times, the gas has to be expanded

Two spherical black bodies of radii '$$r_1$$' and '$$r_2$$' at temperature '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' respectively radiate power in the ratio $$1: 2$$ Then $$r_1: r_2$$ is

The rate of flow of heat through a metal rod with temperature difference $$40^{\circ} \mathrm{C}$$ is $$1600 \mathrm{~cal} / \mathrm{s}$$. The thermal resistance of metal rod in $${ }^{\circ} \mathrm{C} \mathrm{s} / \mathrm{cal}$$ is