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A solid aluminum sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed cool under identical surrounding temperature. Assume that the emissivity of both the sphere is the same. Find the ratio of (a) the rate of heat loss from the aluminum sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminum sphere to the rate of fall of temperature of the copper sphere. The specific heat capacity of aluminum = 900 J/kg-°C and that of copper = 390 J/kg-°C. The density of copper = 3.4 times the density of aluminum.

A solid aluminum sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed cool under identical surrounding temperature. Assume that the emissivity of both the sphere is the same. Find the ratio of (a) the rate of heat loss from the aluminum sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminum sphere to the rate of fall of temperature of the copper sphere. The specific heat capacity of aluminum = 900 J/kg-°C and that of copper = 390 J/kg-°C. The density of copper = 3.4 times the density of aluminum.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Sol. E → Energy radiated per unit area per unit time Rate of heat flow → Energy radiated (a) Per time = E × A So, E base AI = eσT^4 * A/eσT^4 * A = 4πr^2/4π(2r)^2 = 1/4 ∴ 1 : 4 (b) Emissivity of both are same = m base 1S base 1dT base 1/m base 2S base 2dT base 2 = 1 ⇒ dT base 1/dT base 2 = m base S base 2/m base 1S base 1 = s base 14πr base 1^3 * S base 2/s base 24πr base 2^3 * S base 1 = 1 * π * 900/3.4 * 8π * 390 = 1 : 2 : 9

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