Question

Two spheres $P\text{and}Q$ of same colour having radius $8cm\text{and}2cm$ are maintained at temperature ${127}^{\circ }\text{and}{527}^{\circ }C$ respectively. The ratio of energy radiated by $P\text{and}Q$ is-

• A. 0.054
• B. 0.0034
• C. 1
• D. 2

Answer 1

Answer: (C)

1

Total energy radiated by body in time t = Q = $ϵ\sigma A{T}^{4}t$

where $A$ is the surface area of the radiating body.

Thus $\frac{Q_1}{Q_2}=\frac{{r_1}^2{T_1}^4}{{r_2}^2{T_2}^4}$ $={\left(\frac{8}{2}\right)}^2{\left(\frac{127+273}{527+273}\right)}^4=1$