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10-2.Transmission of Heat
normal
A sphere and cube made of same material and having same surface area are heated to the same temperature and kept in the same surrounding. The ratio of their initial rates of cooling will be
A
$\sqrt {\frac{\pi }{6}} :1$
B
$\sqrt {\frac{\pi }{2}} :1$
C
$\sqrt {\frac{\pi }{3}} :1$
D
$\frac{\pi }{{\sqrt 3 }}:1$
Solution
$\mathrm{R}_{\mathrm{f}}=\frac{\mathrm{e}_{\mathrm{x}} \sigma \mathrm{A}\left[\mathrm{T}^{4}-\mathrm{T}_{0}^{4}\right]}{\mathrm{ms}}=\frac{\mathrm{e}_{\mathrm{r}} \sigma \mathrm{A}\left[\mathrm{T}^{4}-\mathrm{T}_{0}^{4}\right]}{\mathrm{v} \rho \mathrm{s}}$
$\mathrm{R}_{\mathrm{f}} \propto \frac{1}{\mathrm{V}} \Rightarrow \frac{\mathrm{R}_{\mathrm{fsphere}}}{\mathrm{R}_{\mathrm{fcube}}}=\frac{\mathrm{a}^{3}}{\frac{4}{3} \pi \mathrm{r}^{3}}$
Standard 11
Physics
