Heat Transfer - Radiation

The left end of a copper rod (length = 20 cm, area of cross section = 0.20 cm²) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation, find (a) the temperature at a point 11 cm from the left end and (b) the heat current through the rod. Thermal conductivity of copper = 385 W m⁻¹°C⁻¹.

Assume that the total surface area of a human body is 1.6 m² and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is 37°C. Stefan constant σ is 6.0 × 10⁻⁸ W m⁻² K⁻⁴.

A spherical ball A of surface area 20 cm² is kept at the centre of a hollow spherical shell B of area 80 cm². The surface of A and the inner surface of B emit as blackbodies. Both A and B are at 300 K. (a) How much is the radiation energy emitted per second by the ball A? (b) How much is the radiation energy emitted per second by the inner surface of B? (c) How much of the energy emitted by the inner surface of B falls back on this surface itself?

A cylindrical rod of length 50 cm and cross sectional area 1 cm² is fitted between a large ice chamber at 0°C and an evacuated chamber maintained at 27°C as shown in the figure. Only small portions of the rod are inside the chamber and the rest is thermally insulated from the surrounding. The cross section going into the evacuated chamber is blackened so that it completely absorbs any radiation falling on it. The temperature of the blackened end is 17°C when steady state is reached. Stefan constant σ = 6 × 10⁻⁸ W m⁻² K⁻⁴. Find the thermal conductivity of the material of the rod.

A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identically surrounding temperatures. Assume that the emissivity of both the spheres in the same. Find the ratio of (a) the rate of heat loss from the aluminium sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminium sphere to the rate of fall of temperature of the copper sphere. The specific heat capacity of aluminium = 900 J kg⁻¹°C⁻¹ and that of copper = 390 J kg⁻¹°C⁻¹. The density of copper = 3.4 times the density of aluminium.

Why does blowing over a spoonful of hot tea cools it? Does evaporation play a role? Does radiation play a role?

Two identical metal balls one at T₁ = 300 K and the other at T₂ = 600 K are kept at a distance of 1 m in a vacuum. Will the temperatures equalise by radiation? Will the rate of heat gained by the colder sphere be proportional to `t_2^4 - t_1^4` as may be expected from the Stefan's law?

Standing in the sun is more pleasant on a cold winter day than standing in shade. Is the temperature of air in the sun considerably higher than that of the air in shade?