Question

The temperature of a body is increased from -173 C to 357 C. What is the ratio of energies emitted by the body per second in these two cases?

Answer 1

QUESTION:

The temperature of a body is increased from -173 C to 357 C. What is the ratio of energies emitted by the body per second in these two cases?

ANSWER

According to the Stefan-Boltzmann law the total energy radiated per unit surface area of a black body across all wavelengths per unit time is $\varepsilon = \sigma T^4$

Hence (-173 C = 100 K, 357 C = 630 K)

$$\frac{\varepsilon_1}{\varepsilon_2} = \left(\frac{T_1}{T_2}\right)^4$$ $$\frac{\varepsilon_1}{\varepsilon_2} = \left(\frac{100}{630}\right)^4 = 6.348 \cdot 10^{-4}$$

ANSWER

$$\frac{\varepsilon_1}{\varepsilon_2} = 6.348 \cdot 10^{-4}$$