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A solid aluminium sphere and a solid copper sphere whose radius is twice that of the aluminium sphere are heated to the same temperature and then allowed to cool in identical surroundings. The emissivity of both spheres is the same. Given specific heat capacity of aluminium = 900 J/kg-degC, of copper = 390 J/kg-degC, and density of copper = 3.4 times the density of aluminium, find (a) the ratio of the rate of heat loss of the aluminium sphere to that of the copper sphere, and (b) the ratio of the rate of fall of temperature of the aluminium sphere to that of the copper sphere.
- (a) 1/4 and (b) 2.95
- (a) 1/2 and (b) 1.47
- (a) 1/4 and (b) 0.34
- (a) 1/8 and (b) 2.95
Correct answer: (a) 1/4 and (b) 2.95
Solution
By Stefan's law the rate of heat loss is proportional to the surface area when emissivity, body temperature and surroundings are identical. Surface area scales as r², so the larger copper sphere loses heat faster. The rate of fall of temperature is the heat-loss rate divided by the heat capacity (mass times specific heat), and mass scales as density times r³, so this ratio depends on density, radius and specific heat.
Related JEE Advanced Physics questions
- Match the temperature of a blackbody listed in Group-I to the corresponding statement in Group-II, and select the correct answer.
[Given: Wien’s constant = 2.9 × 10⁻³ m-K and hc/e = 1.24 × 10⁻⁶ V-m]
Group-I:
(P) 2000 K
(Q) 3000 K
(R) 5000 K
(S) 10000 K
Group-II:
(1) The peak wavelength of emitted radiation can cause photoelectron ejection from a metal with a work function of 4 eV.
(2) The peak wavelength of emitted radiation falls within the visible spectrum.
(3) The peak wavelength of emitted radiation produces the broadest central diffraction maximum in a single-slit setup.
(4) The energy radiated per unit area is one-sixteenth of that emitted by a blackbody at 6000 K.
(5) The peak wavelength of emitted radiation is suitable for imaging human bones.
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