Question

If the radiant temperature of a body is 360 K and its emissivity is 0.6, then the kinetic temperature of that body is _______ K (Answer in integer).}

Hint:

Radiant temperature is related to kinetic temperature via \( T_r^4 = \varepsilon T_k^4 \). Use this to find true physical temperature when emissivity is known.

Answer 1

The relationship between radiant temperature ($T_r$), emissivity ($\varepsilon$), and kinetic temperature ($T_k$) is given by: \[ T_r^4 = \varepsilon \cdot T_k^4 \] Rearranging to solve for $T_k$: \[ T_k = \left( \frac{T_r^4}{\varepsilon} \right)^{1/4} = \left( \frac{360^4}{0.6} \right)^{1/4} = \left( \frac{1.6796 \times 10^{10}}{0.6} \right)^{1/4} = \left( 2.7993 \times 10^{10} \right)^{1/4} \approx 409.6\ {K} \] So, the kinetic temperature is approximately: \[ \boxed{410\ {K}} \]