# Heating of sphere through resistor!

Classical Mechanics Level 4

A highly conducting uniform sphere of thermal capacity $$C$$ is heated by an electric heater, a resistance $$R$$ fitted within the sphere. A constant current $$I$$ is passed through the heater starting at time $$t = 0$$ which gives constant power . The sphere loses heat at a rate equal to $$k$$ times the temperature difference between the sphere and the surrounding. The initial temperature of the sphere and that of the surrounding is $$0°C$$.

The time at which sphere attains half of its maximum attainable temperature is $$\frac{c}{k}\ln 2^a$$. Then find the value of "$$a$$".

×