A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identical surrounding temperatures. Assume that the emissivity of both the spheres is the same. Find ratio of (a) the rate of heat loss from the aluminium sphere to the rate of all of temperature of the copper sphere. The specific heat capacity of aluminium `=900Jkg^(-1)`^(@)C^(-1)`. and that of copper =`390Jkg^(-1)`^(@)C^(-1)` . The density of copper =3.4 times the correct wattage.

Answer

A, B, D

Explanation

E=Energy radiated per unit area per unit time
Rate of heat flow =Energy radiated
(a) Energy per unit time` =ExxA`
`So, E_(Al)=(eOT^4xxA)/(eOT^4xxA')`
`=(4 pi r^2)/(4pi (2r)^2)=1:4`
`(b) Emissivity of both are same`
` (M_1s_2dT_1)/(M_1s_2dT_2)=1`
`implies (dT_1)/(dT_2)=(M_2s_2)/(M_1s_1)`
=(rho_(2)4 pi r_(2)^(3)xxs_2)/(rho_(1)4 pi r_(1)^(3)xxs_(1))`
`(1xx3.4xx8 pi xx390)/(4xx1xxpixx90)`
`2.9:1`.