Calculate the amount of heat radiated per second by a body of surface area 12 cm² kept in thermal equilibrium in a room at temperature 20°C. The emissivity of the surface = 0.80 and σ = 6.0 × 10⁻⁸ W m⁻² K⁻⁴.

Figure shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross-section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.

Two bodies of masses m₁ and m₂ and specific heat capacities s₁ and s₂ are connected by a rod of length ℓ, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the firs body is T₁ and the temperature of the second body is T₂(T₂> T₁). Find the temperature difference between the two bodies at time t.

An amount n (in moles) of a monatomic gas at an initial temperature T₀ is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature T_s(>T₀) and the atmospheric pressure is p_a. Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all changes to be slow, find the distance moved by the piston in time t.

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.