Question

A black body rediates energy at the rate of E watt per metre² at a high temperature T K. When the temperature is reduced to (T/2) K, the radiant energy will be(a) E/16(b) E/4(c) E/2(d) 2E

Answer 1

Answer:

A] E/16

Explanation:

Energy rate = E watt per metre²

Temperature = TK

As per the Stefan Boltzmann law the radiated energy per unit time also knows as power across all the wavelengths from a black body at a temperature T °K is denoted as

=  - J = σ T⁴ 

Where σ = Stefan Boltzmann's constant

= 5.67 * 10⁻⁸ Wb /m²/K⁻⁴

Given   J = E = σ T⁴

When T becomes T/2 °K,  then  

 J = σ T⁴/2⁴ = E/16

So the radiated power (energy/time) will become 1/16 th of E.

Thus, the radiant energy will be E/16