Ratio of emissive power at two temperatures

The emissive power of a black body is given by the Stefan-Boltzmann law, which states that the power radiated by a black body per unit surface area is proportional to the fourth power of its absolute temperature. Mathematically, it can be expressed as:

E = σT^4

where E is the emissive power, σ is the Stefan-Boltzmann constant, and T is the temperature in Kelvin.

Given that the temperature of the black body increases from -73 degrees Celsius to 327 degrees Celsius, we need to convert these temperatures to Kelvin before calculating the ratio of emissive powers.

Converting temperatures to Kelvin

To convert a temperature from degrees Celsius to Kelvin, we can use the formula:

T(K) = T(°C) + 273.15

For the initial temperature of -73 degrees Celsius:

T1(K) = -73 + 273.15 = 200.15 K

For the final temperature of 327 degrees Celsius:

T2(K) = 327 + 273.15 = 600.15 K

Calculating the ratio of emissive powers

Now that we have the temperatures in Kelvin, we can use the Stefan-Boltzmann law to calculate the emissive powers at both temperatures.

E1 = σT1^4
E2 = σT2^4

Taking the ratio of these two emissive powers:

E2/E1 = (σT2^4)/(σT1^4)
E2/E1 = (T2/T1)^4

Substituting the values of the temperatures:

E2/E1 = (600.15 K/200.15 K)^4

Calculating the ratio:

E2/E1 = (3)^4 = 81

Therefore, the ratio of emissive power at the two temperatures is 81.

Conclusion

The ratio of emissive power at -73 degrees Celsius and 327 degrees Celsius is 81. This means that as the temperature of a black body increases, the emissive power increases significantly, following the fourth power relationship described by the Stefan-Boltzmann law.