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Mechanical Properties Of Fluids

Question
CBSEENPH11019837

A body of surface area A and emissivity e is heated to a temperature T and placed in an enclosure maintained at temperature T0 (T0<T). Find the net rate of loss of heat by the body by radiation.

Solution
According to Stefan’s law, at temperature T, the energy emitted per second per unit area by black body is,
                              straight E equals σT to the power of 4
Therefore heat energy emitted by any body at temperature T per second is given by, 
                          straight E subscript c equals eAσT to the power of 4 
According to Prevost’s theory, due to temperature of enclosure, body absorbs the thermal radiation.
Therefore, due to temperature T0 of enclosures, the heat energy absorbed by body per second is,
                    space space space space space straight E subscript straight a equals eAσT subscript 0 superscript 4
Net heat lost by body at T placed in enclosure at temperature T is,
negative dQ over dt equals straight E subscript straight c minus straight E subscript straight a equals eAσT to the power of 4 minus eAσT subscript 0 superscript 4 
         equals eAσ left parenthesis straight T to the power of 4 minus straight T subscript 0 superscript 4 right parenthesis 
Negative sign mplies heat lost by the body.