A liquid-nitrogen container is constructed from a 1 -cm thick styrofoam sheet with a thermal conductivity of 0.025 J s ⁻¹ m ⁻¹ ^ C ⁻¹ . Liquid nitrogen at 80 K is stored inside. A total area of 0.80 m ^2 is in contact with the liquid nitrogen. Given that the atmospheric temperature is 300 K , determine the rate of heat flow from the atmosphere into the liquid nitrogen.

Step-by-step solution

The rate of heat flow through the styrofoam sheet is given by Fourier's law of heat conduction: dQ dt = KA(T₂ - T₁) d Given values are: Thermal conductivity, K = 0.025 J s ⁻¹ m ⁻¹ ^ C ⁻¹ Area, A = 0.80 m ^2 Temperature difference, T = T₂ - T₁ = 300 K - 80 K = 220 K Thickness, d = 1 cm = 0.01 m Substituting these values into the formula: dQ dt = 0.025 0.80 220 0.01 dQ dt = 0.02 220 0.01 dQ dt = 4.4 0.01 = 440 J s ⁻¹