A solid receives heat by radiation over its surface at the rate of $4 k W$ . The heat convection rate from the surface of solid to the surrounding is $5.2 k W$ , and heat is generated at a rate of $1.7 k W$ over the volume of the solid. The rate of change of the average temperature of the solid is ${0.5}^{\circ} C s^{- 1}$ . Find the heat capacity of the solid.

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Solution

$H_{R a d i a t i o n} + H_{G e n e r a t e d} - H_{C o n v e c t i o n} = H_{R e t a i n e d}$
$4 + 1.7 - 5.2 = 0.5 k W = 0.5 \times 10^{3} W = H_{R e t a i n e d}$
Heat Capacity $C = \frac{H_{R e t a i n e d}}{Δ T}$
Substituting $Δ T = 0.5$ as given
$C = \frac{0.5 \times 10^{3}}{0.5} = 1000 J /^{0} C$

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HRadiation+HGenerated−HConvection=HRetained4+1.7−5.2=0.5kW=0.5×103W=HRetainedHeat CapacityC=HRetainedΔTSubstituting ΔT=0.5 as givenC=0.5×1030.5=1000J/0C