The concrete wall of a building is 0.09 m thick. The temperature inside the buil

Question

The concrete wall of a building is 0.09 m thick. The temperature inside the building is 21.5 °C, while the temperature outside is 0.0 °C. Heat is conducted through the wall. When the building is unheated, the inside temperature falls to 0.0 °C, and heat conduction ceases. However, the wall does emit radiant energy when its temperature is 0.0 °C. The radiant energy emitted per second per square meter at 0.0 °C is the same as the heat lost per second per square meter due to conduction when the temperature inside the building is 21.5 °C. What is the emissivity of the wall?

Explanation / Answer

Any object having surface emmisivity (e), temp (T=273 K) will radiate heat per sec (Q-dot in J/s) to its surroundings as per

Q-dot = e * sigma* A * (T^4)
Heat radiated/area/sec = Qr = Q-dot/A
Qr = e * sigma*(T^4) -------(1)
where sigma = stefan's constant, A =cross-section area
stefan's law takes temp in deg Kelvin
======================================...
Prevost theory of heat exchange says that even when all objects in a room are at equilibrium temp (T) they exchange heat energies with each other ... only thing important is that they give as much as they recive >> that's why temp (T) remains same inside
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heat conducted thro wall per sec = k A (21.5 - 0) /x
so per unit area, Qc = k (21.5 - 0) /x
Qc = k (21.5 - 0) /0.09
Qc = 238.88 k ----------(2)

given Qr = Qc
e * sigma*(T^4) = 238.8 k
e = 238.8 k / sigma*(T^4) = 238.8k / sigma*(273^4)
======
sigma = 5.67*10^-8 W/m^2-K^4
k = conductivity of concrete = k concrete = 0.872 W/m.K
============
e = 238.8 *0.872 / 5.67*10^-8*(273^4)
e = 0.661

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