SATHEE: Properties Of Solids And Liquids Question 444

Properties Of Solids And Liquids Question 444

Question: A sphere and a cube of same material and same volume are heated upto same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted will be

Options:

A) 1 : 1

B) $\frac{4 π}{3} : 1$

C) ${(\frac{π}{6})}^{1 / 3} : 1$

D) $\frac{1}{2} {(\frac{4 π}{3})}^{2 / 3} : 1$

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Answer:

Correct Answer: C

Solution:

[c] $Q = σ A t (T^{4} - T_{0}^{4})$ If $T, T_{0}, σ$

and t are same for both bodies, then $\frac{Q_{s p h e r e}}{Q_{c u b e}} \frac{A_{s p h e r e}}{A_{c u b e}} = \frac{4 π r^{2}}{6 a^{2}}$

But according to problem, Volume of sphere = Volume of cube $\Rightarrow \frac{4}{3} π r^{3} = a^{3} \Rightarrow a = r {(\frac{4}{3} π)}^{1 / 3}$

Substituting the value of a in equation (i), we get $\frac{Q_{s p h e r e}}{Q_{c u b e}} = \frac{4 π r^{2}}{{6 {(\frac{4}{3} π)}^{1 / 3} r}^{2}} = {(\frac{π}{6})}^{1 / 3} : 1$

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Properties Of Solids And Liquids Question 444

Question: A sphere and a cube of same material and same volume are heated upto same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted will be

Options:

Answer:

Solution:

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