A cylinder of radius $$r$$ and of thermal conductivity $$K_1$$ is surrounded by a cylindrical shell of inner radius $$r$$ and outer radius $$2 r$$ made of a material of thermal conductivity $$K_2$$. The effective thermal conductivity of the system is

In an adiabatic expansion of air, the volume is increased by $$6.2 \%$$. The percentage change in pressure is $$(\gamma=1.4)$$

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in internal energy of a mass of a gas when the volume changes from $$\mathrm{V}$$ to $$3 \mathrm{~V}$$ at constant pressure is

The molecules of a given mass of a gas have root mean square speed of $$120 \mathrm{~m} / \mathrm{s}$$ at $$88^{\circ} \mathrm{C}$$ and 1 atmospheric pressure. The root mean square speed of the molecules at $$127^{\circ} \mathrm{C}$$ and 2 atmospheric pressure is