A radiometer has two square vanes (1.0 cm by 1.0 cm),attached to a light horizontal cross arm,and pivoted about a vertical axis through the center,as shown in the figure.The center of each vane is 6.0 cm from the axis.One vane is silvered and it reflects all radiant energy that falls upon it.The other vane is blackened and it absorbs all incident radiant energy.Radiant energy,having an intensity of 300 W/m²,is incident normally upon the front surfaces of both vanes.What is the radiant power absorbed by the blackened vane? A)0.030 W B)0.040 W C)0.050 W D)0.060 W E)0.090 W

Question

Quizplus · Accepted Answer

Since the radiant energy is incident normally on the front surfaces of both vanes, the intensity of the incident radiation is the same for both vanes. The silvered vane reflects all incident radiant energy so it does not absorb any radiant power. On the other hand, the blackened vane absorbs all incident radiant energy.

The radiant power absorbed by the blackened vane can be calculated as follows:

Power absorbed = Intensity x Area of vane

The area of each vane is given by:

Area = length x width = 1.0 cm x 1.0 cm = 0.01 cm^2

Converting the area to m^2:

Area = 0.01 cm^2 x (1 m/100 cm)^2 = 1.0 x 10^-6 m^2

The intensity of the incident radiation is given by:

Intensity = 300 W/m^2

Therefore, the radiant power absorbed by the blackened vane is:

Power absorbed = Intensity x Area of vane 
                             = (300 W/m^2) x (1.0 x 10^-6 m^2) 
                             = 0.0003 W

Rounding off to three significant figures, the answer is:

Power absorbed ≈ 0.030 W

A Radiometer Has Two Square Vanes (1