A black body of mass 34.38 g and surface area 19.2 $cm^{2}$ is at an initial temperature of 400 K. It is allowed to cool inside an evacuated enclosure kept at constant temperature 300 K. The rate of cooling is 0.04$℃s^{- 1}$. The specific heat of the body in $J\ kg^{- 1}K^{- 1}$ is (Stefan’s constant $\sigma = 5.73 imes 10^{- 8}\ Wm^{- 2}K^{- 4}$)

Question

A black body of mass 34.38 g and surface area 19.2 $cm^{2}$ is at an initial temperature of 400 K. It is allowed to cool inside an evacuated enclosure kept at constant temperature 300 K. The rate of cooling is 0.04$℃s^{- 1}$. The specific heat of the body in $J\ kg^{- 1}K^{- 1}$ is (Stefan’s constant $\sigma = 5.73 	imes 10^{- 8}\ Wm^{- 2}K^{- 4}$)

Dr. Abubacker · Accepted Answer

(c) According toNewtons’s law of cooling
$\frac{d	heta}{dt} = \frac{\sigma A(T^{4} - T_{0}^{4})}{ms}$
$	herefore$ Specific heat s= $\frac{\sigma A(T^{4} - T_{0}^{4})}{m\left( \frac{d	heta}{dt} ight)}$
Substituting the values
$	herefore\ \ s = \frac{\begin{array}{r}
\left( 5.73 	imes 10^{- 8} ight)\left( 19.2 	imes 10^{- 4} ight)\left\lbrack (4)^{4} - (3)^{4} ightbrack \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  	imes 10^{8}
\end{array}}{\left( 34.38 	imes 10^{- 3} ight)(4 	imes 10^{- 2})} = 1400$

Explanation

Reviewed by Dr. Abubacker

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