Question

In the 25 ftft Space Simulator facility at NASA's Jet Propulsion Laboratory, a bank of overhead arc lamps can produce light of intensity 2500 W/m^2 at the floor of the facility. (This simulates the intensity of sunlight near the planet Venus.)
Required:
Find the average radiation pressure (in pascals and in atmospheres) on

a. A totally absorbing section of the floor.
b. A totally reflecting section of the floor.
c. Find the average momentum density (momentum per unit volume) in the light at the floor.

Answer 1

Answer:

a) 8.33 x $10^{-6}$ Pa  or  8.22 x $10^{-11}$ atm

b) 1.66 x $10^{-5}$ Pa  or  1.63 x $10^{-10}$ atm

c) 2.77 x $10^{-14}$ kg/m^2-s

Explanation:

Intensity of light = 2500 W/m^2

area = 25 ft^2

a) average radiation pressure on a totally absorbing section of the floor$Pav = \frac{I}{c}$

where I is the intensity of the light

c is the speed of light = $3*10^{8} m/s$

$Pav = \frac{2500}{3*10^{8} }$ = 8.33 x $10^{-6}$ Pa

1 pa = $9.87*10^{-6}$

8.33 x $10^{-6}$ Pa = 8.22 x $10^{-11}$ atm

b) average radiation for a totally radiating section of the floor

$Pav = \frac{2I}{c}$

this means that the pressure for a totally radiating section is twice the average pressure of the totally absorbing section

therefore,

Pav = 2 x 8.33 x $10^{-6}$  = 1.66 x $10^{-5}$ Pa

or

Pav in atm = 2 x 8.22 x $10^{-11}$ = 1.63 x $10^{-10}$ atm

c) average momentum per unit volume is

$m = \frac{I}{c^{2} }$

$m = \frac{2500}{(3*10^{8}) ^{2} }$ = 2.77 x $10^{-14}$ kg/m^2-s