Discussed previously all things that have temperature radiate. The amount of energy given off by an object is according to the fourth power of its absolute temperature

eq8.1Lesson8.gif

Equation 9.1

where Tk is degrees Kelvin. To convert from a room temperature of 68°F (20°C) to absolute temperature (or Kelvin scale), add 273 to the Celsius value. Therefore, the Kelvin scale room temperature is 293°K. To find the amount of energy given off by something, take its Kelvin temperature to the fourth power. Then multiply it times the Stefan-Boltzmann's constant, sigma, named after the people who came up with this relationship, and a factor called emissivity, epsilon. Emissivity is a number that varies from 0 to 1 (will be discussed later in the lesson). Thus, the total energy radiated is given by the equation

eq8.2Lesson8.gif

Equation 9.2

The Stefan-Boltzmann constant converts to units of energy (watts, ergs or calories according to the unit system being used). The important thing to remember is that the amount of energy given off by something is proportional to the fourth power of its absolute temperature.

Study Question 9.3
How much energy is given off by a box at room temperature with an emissivity of 0.95?
Stephan-Boltzman constant: 5.67 x 10-8 Wm-2 K-4
Wm-2  

How much energy is given off by the sun (temperature 6000 K) with an emissivity of 0.99?

Wm-2  

This relationship explains many things about the amount of heat given off by items.

Quite often you won't need to know too much about the quantity of energy. What you need to know is the temperature. If something is radiating according to this same rule, we will have to look at two temperatures. As displayed in Equation 9.2, the emissivity reduces the energy output of the object. The temperature sensed will be called the apparent temperature, Tapp. The apparent temperature will appear lower because of the radiation reduction by the emissivity. The apparent temperature raised to the fourth power (Tapp4) will equal the emissivity, times the true temperature (Ttrue4) raised to the fourth power. The value that a satellite sees is the apparent temperature. If a satellite was looking at the ground of actual temperature 294 K, the satellite would see some apparent temperature (call it Tapp , without the 4th power) which equals the 4th root of the emissivity of the surface of the fourth power of the true temperature.

Study Question 9.4
What temperature would a satellite see looking at a surface with an emissivity of 0.96 and a temperature of 270 K?
K