Edexcel A Level Physics:復(fù)習(xí)筆記9.11 Stefan-Boltzmann Law
Stefan-Boltzmann Law
- An objects?luminosity?depends on two factors:
- Its surface temperature
- Its surface area
- The relationship between these is known as the?Stefan-Boltzmann Law, which states:
The total energy emitted by a black body per unit area per second is proportional to the fourth power of the absolute temperature of the body
- So,?L?∝?AT4
- The Stefan-Boltzmann Law equation is:
L = σAT4
- Where:
- L?=?luminosity?of the star (W)
- A?= surface area of the star
- σ = the?Stefan-Boltzmann constant
- T?= surface temperature of the star (K)
- The surface area of a star (or other spherical object) can be calculated using:
A =?4πr2
- Where:
- r =?radius of the star
Worked Example
A camel has a body temperature of 40 ?C and a surface area of 16 m2. The peak wavelength of the emitted spectrum from the camel is λmax?= 8.6 × 10–6?m. Calculate the total power radiated by the camel.
Step 1: Write down the equation
L = σAT4
Step 2:?Convert temperature from ?C to K
-
- 40 + 273 = 313 K
Step 3: Substitute in the values
-
- L?= (5.67 × 10–8) × 16 × 3134?= 29387 W = 8 707
Step 4: Write answer to correct significant figures and include units
Luminosity (power emitted) of the camel = 8 700 W (2 sig figs)
Exam Tip
Remember to convert temperatures into Kelvin.
If you are given the radius of a spherical object then its surface area?A?can be calculated using?A =?4πr2?for the radius of the object?r.
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