A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside

PHYSICS · Single correct · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature

T_0

. The initial temperature of the sphere is

3T_0

. If the specific heat of the material of the sphere varies as

\alpha T^3

per unit mass with the temperature T of the sphere, where

\alpha

is a constant, then the time taken for the sphere to cool down to temperature

2T_0

will be (

\sigma

is Stefan Boltzmann constant). (1)

\frac{M\alpha}{4\pi R^2 \sigma} \ln\left(\frac{3}{2}\right)

(2)

\frac{M\alpha}{4\pi R^2 \sigma} \ln\left(\frac{16}{3}\right)

(3)

\frac{M\alpha}{16\pi R^2 \sigma} \ln\left(\frac{16}{3}\right)

(4)

\frac{M\alpha}{16\pi R^2 \sigma} \ln\left(\frac{3}{2}\right)