A liquid-nitrogen container is made of a 1 cm thick Styrofoam sheet having thermal conductivity 0.025 J s–1m–1°C–1. Liquid nitrogen at 80 K is kept in it. A total area of 0.80 m2 is in contact with the liquid nitrogen. The atmospheric temperature is 300 K. Calculate the rate of heat flow from the atmosphere to the liquid nitrogen.
Given:
Thickness of the container : x = 1 cm = 0.01 m
Thermal conductivity of the sheet : K= 0.025 J s–1m–1°C–1
Temperature of the liquid nitrogen: T1 = 80 K
Area of the container : A = 0.8 m2
Temperature of the atmosphere : T2 = 300 K
Formula used:
Rate of amount of heat flowing is given as:
Here, Δθ is the amount of heat transferred, ΔT is the temperature difference, K is the thermal conductivity of the material, A is the area of cross section of the material and x is the thickness of the material.
Here, ΔT = T2- T1 = 220 K
Substituting the values we get,
Hence, the rate of heat flow from the atmosphere to the liquid nitrogen is 440 J/s.