The Stefan-Boltzmann Law
Power is measured in Watts
Power is energy produced in 1
second
Joseph Stefan thought about the power
produced per metre squared of a black
body
W
m2
The Stefan-Boltzmann Law
Power
output
per
square
metre
P
4

T
2
m
Wm-2
Temperature K
Joseph Stefan (Austria 1879) found the
relationship between the temperature of a black
body and the power output per square metre
The Stefan-Boltzmann Law
Power
Output
Per
square
metre
(Wm-2)
This is a straight line
graph the gradient is a
constant (σ) called the
Stefan-Boltzmann
constant.
(Temperature)4
 p 
 2
m  
4
T
 p 
 2
m  
4
T
The Power of a STAR is called its
luminosity
P  AT
P
4


T
2
m
P  T  m
4
2
P  T  surface area
4
4
P  T 4  surface area
Stars are just about spherical.
The formula for the surface area of a sphere
surface area  4r 2
P  4r T
2
4
Where σ is Stefan’s constant (5.7 x 10-8 Wm-2K-4)
Calculating with Stefan’s Law
The Sun has surface temperature of 5800K. It’s radius is
6.96 x 108m. Calculate its power output.
( the Stefan constant is 5.7 x 10-8 Wm-2K-4)
The Sun like all stars is an almost spherical black body so:
P  4r 2T 4
P= 4π (6.96 x 108)2 x 5.7 x 10-8 x 58004
P = 3.91 x 1026W
Calculating with Stefan’s Law
A star has a surface
P  4r 2T 4
temperature of 4800K.
P
Its power output is known to r 2 
be 3.2 x 1028 Watts.
4T 4
Calculate its radius
P
r
4T 4
3.2 1028
r
4 (5.7 108 )  48004
Compare this with the radius of
the Sun
r= 9.2 x 109m