Hot water cools from $60\,^oC$ to $50\,^oC$ in the first $10\,minutes$ and to $42\,^oC$ in the next $10\,minutes$. The temperature of the surroundings is  ......... $^oC$

A black body has maximum wavelength $\lambda_m$ at $2000\,K$. Its corresponding wavelength at $3000\,K$ will be

A cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

The plots of intensity versus wavelength for three black bodies at temperature $T_1$, $T_2$ and $T_3$ respectively are as shown. Their temperatures are such that

Assuming the sun to be a spherical body of radius $R$ at a temperature of $TK$ , evaluate the total radiant power, incident on the earth, at a distance $r$ from the sun, is (Where $r_0$ is the radius of the earth and $\sigma $ is Stefan s constant.)

Two identical conducting rods are first connected independently to two vessels, one containing water at $100^o\ C$ and the other containing ice at $0^o\  C$. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_2\  g/s$ be the rate of melting of ice in the two cases respectively. The ratio $q_2/q_1$ is