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A black body of mass $34.38 \mathrm{~g}$ and surface area $19.2 \mathrm{~cm}^2$ is at an initial temperature of $400 \mathrm{~K}$. It is allowed to cool inside an evacuated enclosure kept at constant temperature $300 \mathrm{~K}$. The rate of cooling is $0.04^{\circ} \mathrm{C}$ per second. The specific heat of the body in $\mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1}$ is
(Stefan's constant $\sigma=5.73 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$
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(Stefan's constant $\sigma=5.73 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$
Solution:
1106 Upvotes
Verified Answer
The correct answer is:
$1400$
$$
\frac{d \theta}{d t}=\frac{\sigma A\left(T^4-T_0^4\right)}{m s}
$$
$\therefore$ Specific heat $s=\frac{\sigma A\left(T^4-T_0^4\right)}{m\left(\frac{d \theta}{d t}\right)}$
Substituting the values
$$
\begin{aligned}
& s=\frac{\left(5.73 \times 10^{-8}\right)\left(19.2 \times 10^{-4}\right)\left[(4)^4-(3)^4\right] \times 10^8}{\left(34.38 \times 10^{-3}\right)\left(4 \times 10^{-2}\right)} \\
& \therefore \quad s=1400 \\
&
\end{aligned}
$$
\frac{d \theta}{d t}=\frac{\sigma A\left(T^4-T_0^4\right)}{m s}
$$
$\therefore$ Specific heat $s=\frac{\sigma A\left(T^4-T_0^4\right)}{m\left(\frac{d \theta}{d t}\right)}$
Substituting the values
$$
\begin{aligned}
& s=\frac{\left(5.73 \times 10^{-8}\right)\left(19.2 \times 10^{-4}\right)\left[(4)^4-(3)^4\right] \times 10^8}{\left(34.38 \times 10^{-3}\right)\left(4 \times 10^{-2}\right)} \\
& \therefore \quad s=1400 \\
&
\end{aligned}
$$
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