Question

The temperature of an isolated black body falls from T₁ to T₂ in time t. Let c be a constant.

(a) t = c [1/T₂ - 1/T₁]

(b) t = c [1/T₂² - 1/T₁²]

(c) t = c [1/T₂³ - 1/T₁³]

(d) t = c [1/T₂⁴ - 1/T₁⁴]

Answer 1

Correct Answer is: (c) t = c [1/T₂³ - 1/T₁³]

P = (4πr²)(σT⁴) = ms (- dT/dt) = - 4/3 πr³ ρs. dT/dt

Here, R = dT/dt.

 P ∝ r² and R ∝ 1/r.