JEE Main 2025 Jan 22 Shift 1, Physics Q5: Heat Transfer

JEE Main2025Jan 22, Shift 1Physics

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 bigger body is 400 K. If the energy radiate from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding to be negligible)

A
256 E
B
E
C
64 E
D
16 E

Solution

By Stefan-Boltzmann, $P = σ e A T^{4} \propto r^{2} T^{4}$ .

$\frac{P _{s ma l l}}{P _{l a r g e}} = \frac{( 0.2 ) ^{2} ( 800 ) ^{4}}{( 0.8 ) ^{2} ( 400 ) ^{4}} = \frac{1}{16} \times 2^{4} = \frac{16}{16} = 1$ .

Hence both spheres radiate the same power: energy from the larger body $= E$ .

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JEE Main 2025 Jan 22 Shift 1, Physics Q5: Heat Transfer

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