Question

A black body of mass $34.38$ g and surface area $19.2$ $c{m}^2$ 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 $0.04$ ${}^{0}C$ per second. The specific heat of the body in $Jk{g}^{-1}{K}^{-1}$ is (Stefan's constant $\sigma =$5.73$\times {10}^{-8}W{m}^{-2}{K}^{-4}$)

• A. 2800
• B. 2100
• C. 1400
• D. 1200

Answer 1

The correct option is C 1400

$m=34.38gm=0.03438KgA=19.2{cm}_2=19.2\times {10}_{-4}{m}_2\sigma =5.73\times {10}_{-8}W{m}_{-2}{K}_{-4}T=400K{T}_0=300K$

rate of cooling=$0.04℃$

emissive power of black body=$1$

rate of cooling=$\frac{eA\sigma }{mc}(T^4-T_0^4)$

$\Rightarrow 0.04=\frac{1\times 19.2\times {10}^{-4}\times 5.73\times {10}^{-8}}{0.03438\times c}({400}^4-{300}^4)\Rightarrow 0.04=\frac{56}{c}\Rightarrow c=\frac{56}{0.04}=1400c=1400J{Kg}^{-1}{K}^{-1}$