Suggested Response - Q1

** Calculate the heat loss due to radiation from the surface of a 100 hL copper kettle at 100°C to a room at 20°C. The surface area of the kettle is 27.5 m2 and the emissivity of copper is 0.03.

Response:

The Stefan-Boltzmann law adapted for net rate of heat exchange between two bodies is:

q space equals space sigma epsilon A space left parenthesis T subscript 2 superscript 4 space minus space T subscript 1 superscript 4 right parenthesis

Where

q is the heat transfer rate by radiation in Js-1

A is the heat transfer area in m2

σ is the Stefan-Boltzmann constant = 5.672 × 10-8 Wm-2 K-4

ε is the emissivity of the surface

T1 and T2 are the temperatures of the emitting surface and surrounding matter in K

Using this equation and the given values in the problem statement, we convert the temperatures to the appropriate units of Kelvin and then we can simply enter the values and calculate.

q space equals space sigma epsilon A space left parenthesis T subscript 2 superscript 4 space minus space T subscript 1 superscript 4 right parenthesis

T subscript 1 space equals space 100 space plus space 273 space equals space 373 space K space semicolon space T subscript 2 space equals space 20 space plus space 273 space equals space 293 space K

q space equals space 5.672 space cross times space 10 to the power of negative 8 end exponent space cross times space 0.03 space cross times space 27.5 space cross times space left parenthesis 293 to the power of 4 space minus space 373 to the power of 4 right parenthesis

q space equals space minus 561 space W

So, the kettle at 100°C is losing 561 J per second of heat to the atmosphere at 20°C. To prevent this heat loss and to protect personnel from the risk of burns from the hot vessel surface it would be sensible to fit the vessel with suitable insulation.  

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