Question

Two bodies P and Q have thermal emissivities of E_P and E_Q respectively. Surface area of these bodies is same and the total radiant power is also emitted at the same rate. If the temperature of P in Kelvin is T_P, then the temperature of Q in Kelvin is –

• A. $\left( \frac{E_{Q}}{E_{P}} \right)^{\frac{1}{4}}$× T_P
• B. $\left( \frac{E_{P}}{E_{Q}} \right)^{\frac{1}{4}}$× T_P
• C. $\left( \frac{E_{Q}}{E_{P}} \right)^{\frac{1}{2}}$× T_P
• D. $\left( \frac{E_{P}}{E_{Q}} \right)^{\frac{1}{2}}$× T_P

Answer 1

Answer: (B)

$\left( \frac{E_{P}}{E_{Q}} \right)^{\frac{1}{4}}$× T_P

Answer 2

Intensity of radiation = eAsT⁴

\ 1 = $\frac{E_{P}}{E_{Q}} \times \left( \frac{T_{P}}{T_{Q}} \right)^{4}$

\ T_Q = $\left( \frac{E_{P}}{E_{Q}} \right)^{1/4} \times T_{P}$