A rigid diatomic gas having molar mass m is contained in an insulated container. The container is moving with velocity V. If it is stopped suddenly, the change in temperature is (R - gas constant)

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

Rate of flow of heat through a cylindrical rod is '$H_1$'. The temperature at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same and if the rate of flow of heat becomes '$H_2$' then $H_2 =$

The energy spectrum of a black body exhibits a maximum around a wavelength '$\lambda$'. The temperature of the black body is now changed such that the energy is maximum around a wavelength $2\lambda/3$. The power radiated by the black body will now increase by a factor