Question

A metal cylinder of mass 0.5 kg is heated electrically by a 12 W heater in a room at ${15}^o$ C. The cylinder's temperature rises uniformly to ${25}^o$ C in 5 min and finally becomes constant at ${45}^o$ C. Assuming that the rate of heat loss is proportional to the excess temperature over the surrounding, find the rate of loss of heat of the cylinder to surroundings at ${20}^{\circ }$C.

Answer 1

At steady state the heat loss by the cylinder will be equal to heat gain by heater.

Room temperature is $T_0={15}^{0}C$

To know the $emissivity$ of the material we have to consider that at ${45}^{0}C$ it become in steady state

so heat loss $H=K(T-T_0)$

$K$ is a proportionality constant and $H$ is rate of heat loss.

At ${45}^{0}C$ it will be $K(45-15)=30Kwatt$

It should be equal to $12W$ so $K=\frac{12}{30}=\frac{2}{5}$

Now for ${20}^{0}c$ the rate of heat loss will be $E=K(20-15)=5K=2Watt$