Thermal Properties of Matter

JEE Main level, single correct, medium

117 of 126

Question 117 of 126

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

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Answer: (B) E

dθdt=σeAT4⇒P∝AT4Psmaller Plarger =(0.2)2×8004(0.8)2×4004116×16=1∴Plarger =Psmaller \begin{aligned} & \frac{\mathrm{d} \theta}{\mathrm{dt}}=\sigma \mathrm{eAT}^4 \Rightarrow \mathrm{P} \propto \mathrm{AT}^4 \\ & \frac{\mathrm{P}_{\text {smaller }}}{\mathrm{P}_{\text {larger }}}=\frac{(0.2)^2 \times 800^4}{(0.8)^2 \times 400^4} \\ & \frac{1}{16} \times 16=1 \\ & \therefore \mathrm{P}_{\text {larger }}=\mathrm{P}_{\text {smaller }}\end{aligned}

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