UPSEE Solved Model Paper 5

The hollow sphere will cool at a faster rate for all values of T
Here, we have to find out the body (hollow sphere or solid sphere) which cools fastly.
We have,
Maximum energy radiated per second
Q = Aεσ(T4−T04) ... (i)
where A - surface of a body
ε - emissivity
σ - stefan's constant
T - temperature at which the body is heated
T0 - temperature of the surrounding
Also,
Let the fall in temperature of the ball be dT. Then heat cost by the body per second
Q = mcdT ... (ii)
where m - mass of the body
c - specific heat capacity
Equating (i) and (ii)
mcdT = Aεσ(T4−T04)
dT =

Aεσ(T4−T04)

mc

That is, the fall in temperature, dT is inversely proportional to the mass of the body.
Since hollow sphere has small mass, fall in temperature will be more.
Therefore, the hollow sphere will cool at a faster rate.