Physical Chemistry , 1st ed.

where the value of this constant is approximately 2898 mK; the wave-

length is in units of micrometers. This equation, enunciated by Wien in

1894, is known as the Wien displacement law. (This relationship is still

used today to estimate the temperature of hot bodies, using an optical

device called a pyrometer to determine intensities of light given off at

certain wavelengths of light.)

Example 9.3

a.What is the total power per unit area emitted by a blackbody at a temper-

ature of 1250 K?

b.If the area of the blackbody is 1.00 cm^2 (0.000100 m^2 ), what is the total

power emitted?

Solution

a.Using equation 9.18 and the value of the Stefan-Boltzmann constant from

above, one finds

total power per unit area (5.6705 

10 ^8 W/m^2 K^4 )(1250 K)^4

The K^4 units cancel to yield

total power per unit area 1.38 

105 W/m^2

b.Since the total power per unit area is 1.38 

105 W/m^2 , for an area of

0.0001 m^2 the power emitted is

power (1.38 

105 W/m^2 )(0.0001 m^2 )

power 13.8 W 13.8 J/s

The definition of the unit “watt” has been used for the final equality to show

that 13.8 joules of energy are emitted per second.

9.7 The Nature of Light 255

0

Wavelength (m)

1000

1500 K

1000 K

2000 K

1.5  104

0

Energy density

1  104

5000

200 400 600 800

Figure 9.12 The experimentally determined behavior of blackbodies. This plot shows the in-
tensity of light at different wavelengths for different temperatures of the blackbody. Explaining
these curves theoretically was a major problem for classical mechanics.