bei48482_FM

If we let h kTx, then kTxh and d (kTh) dx, so that

N 8 V

3



0

The definite integral is a standard one equal to 2.404. Inserting the numerical values of the other

quantities, with V1.00 cm^3 1.00  10 ^6 m^3 , we find that

N2.03  1010 photons

(b) The average energy of the photons is equal to the total energy per unit volume divided by

the number of photons per unit volume:

 

Since a 4 c(see the discussion of the Stefan-Boltzmann law later in this section) and

N(2.405) [8V(kThc)^3 ],

3.73 10 ^20 J0.233 eV

c^2 h^3 T



(2.405)(2k^3 )

aT^4



NV



0

u( ) d

n( )d

x^2 dx



ex 1

kT



hc

Statistical Mechanics 315

A thermograph measures the amount of infrared radiation each

small portion of a person's skin emits and presents this informa-

tion in pictorial form by different shades of gray or different colors

in a thermogram. The skin over a tumor is warmer than elsewhere

(perhaps because of increased blood flow or a higher metabolic

rate), and thus a thermogram is a valuable diagnostic aid for

detecting such maladies as breast and thyroid cancer. A small dif-

ference in skin temperature leads to a significant difference in

radiation rate.

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