A solid aluminium sphere and a solid copper sphere, the latter having twice the radius, are heated to identical temperatures and subsequently allowed to cool in identical surrounding temperatures. Assuming that the emissivity of both spheres is equal, determine the ratio of the rate of heat loss from the aluminium sphere to the rate of heat loss from the copper sphere. The specific heat capacity of aluminium is 900 J

Step-by-step solution

The rate of heat loss from a body is given by the Stefan-Boltzmann law: dQ dt = e A (T^4 - T₀^4) Since both spheres have the same emissivity e , are at identical temperatures T , and are in identical surrounding temperatures T₀ , the rate of heat loss depends only on their surface areas A . The surface area of a sphere is A = 4 R^2 , which implies dQ dt R^2 . Given that the copper sphere has twice the radius of the aluminium sphere, R_ Cu = 2R_ Al . The ratio of the rate of heat loss from the aluminium sphere to th