Question

The ratio of specific heats of two spheres is 2:3, radii 1:2, emissivity 3:1 and density 1:1. Initially, they are kept at same temperatures in atmosphere. Which sphere will cool at a faster rate initially.

Answer 1

Correct Answer - A
In the equation,
`-(dT)/(dt) = (eAsigma)/(mc) (T^4 -T_(0)^4)`
A = surface area `= 4piR^2`
`m = Volume xx density = 4/3 pi R^3rho`
Substituting in the above equation, we have
`-(dT)/(dt) = (3esigma)/(Rrhoc) (T^4 - T_(0)^4) or -(dT)/(dt) prop (e/(Rrhoc))`
Now, `(e/(Rrhoc))_(sphere-1) = 3/(1xx1xx2) = 3/2`
and `(e/(Rrhoc))_(sphere-2) = 1/(2xx1xx3) = 1/6`
`(e/(Rrhoc))` for sphere-1 is more.
So, first sphere will cool at faster rate initially.