A food container has a total area of 0.242 m2. A warm liquid at 42°C is placed in the container. The temperature of the outer wall after thermal equilibrium has been established is found to be 35°C. The container has a thickness of 2.4 mm, and it loses heat to the surroundings at a rate of 191 W. Using this data, determine the thermal conductivity of the material making the container.

An oven has its surface fitted with insulating 0.12 m² rock wool that is 2.0 cm thick. At one instance of the oven's operation, the inner surface of the rock wool is at a temperature of 150°C and the outer surface has a temperature equal to room temperature (25°C). The thermal conductivity of rock wool is 0.040 W/m•K. Determine the heat current flowing through the rock wool insulation. 

During a room heating exercise, a spherical 2.0 L pot is filled with boiling water at 100°C. The emissivity of the pot is 0.55 and the room temperature is 14.0°C. Determine the rate at which the water will lose heat through radiation.

A craftsman fabricates a 50.0 cm long aluminum bar that has a cross-sectional area of 5.07cm². If the bar is used to transfer heat between reservoirs at T_H = 100.0°C and T_C = 25.0°C. Determine the steady-state temperature gradient for the bar. 

Imagine that a spherical iron ball which has a diameter of 5.0 cm is heated and begins to radiate energy at a rate of 850 W. Assuming that the emissivity (e) of iron is 0.7, at what wavelength, in units of μm, does its emission spectrum peak?

A metal plate 25 cm long having a rectangular cross-section of 3.0 cm x 2.0 cm has its ends maintained at 10°C and 150°C. The rate of heat conduction through the rod is 48.4 × 10⁴ J/h. Determine the material of the metal plate.