Question

Two bodies X and Y of identical geometry, mass
surface finish but different material are getting cooled in an atmosphere. Variation of their temperature T with time t is as shown. If Sx and
Sy are their specific heat then​

Answer 1

according to Newton's law of cooling,

$-\frac{dT}{dt}=\frac{4A\epsilon\sigma}{ms}T_s^3\Delta T$

where A is cross sectional area , ε is emissivity of the surface of hot body, $\sigma$ is Stefan's constant , m is mass of body , s is specific heat capacity, $T_s$ is temperature of surrounding and ∆T is change in temperature.

here it is clear that, -dT/dt ∝ 1/s

it means, rate of cooling is inversely proportional to specific heat capacity.

so, higher the negative slope of temperature time graph lower will be specific heat of body.

from figure, it is clearly shown that curve x has higher slope than curve y.

so, specific heat of y > specific heat of x.