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# A Liquid-nitrogen Container is Made of a 1 Cm Thick Styrofoam Sheet Having Thermal Conductivity 0.025 J S−1 M−1 °C−1. Liquid Nitrogen at 80 K is Kept in - Physics

ConceptThermal Expansion of Solids

#### Question

A liquid-nitrogen container is made of a 1 cm thick styrofoam sheet having thermal conductivity 0.025 J s−1 m−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 us 300 K. Calculate the rate of heat flow from the atmosphere to the liquid nitrogen.

#### Solution

Rate of flow of heat =  \text{Temperature  diffrences}/ (Thermal \text{ resistance })

Thickness of the container, l = 1 cm = 10 -2 m
Thermal conductivity of the styrofoam sheet, k = 0.025 J s-1 m-1 °C -1
Area, A= 0.80 m2
Thermal resistance , l/ (KA) = 10^2/(0.025  xx 0.80)

Temperature difference , ΔT = T1 - T2 = 300 - 80 = 220K

Rate of flow of heat, ( (ΔQ )/ (Δt) ) = (T1 - T2)/(l/KA)

⇒ ( (ΔQ )/ (Δt) ) = 440 J / s

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Solution A Liquid-nitrogen Container is Made of a 1 Cm Thick Styrofoam Sheet Having Thermal Conductivity 0.025 J S−1 M−1 °C−1. Liquid Nitrogen at 80 K is Kept in Concept: Thermal Expansion of Solids.
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