   Chapter 27, Problem 100PE

Chapter
Section
Textbook Problem

Integrated Concepts (a) On a day when the intensity of sunlight is 1.00 kW/m2, a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20.0°.Assuming the sunlight is un-polarized and the polarizers are 100% efficient, what is the initial rate of heating of the water in °C/s, assuming it is 80.0% absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

To determine

(a)

Initial rate of heating of the water

Explanation

Given info:

Intensity of sunlight, 1kW/m2

Diameter of the lens, d=0.2m

Angle between the polarizer, θ=20°

Absorption of heat in the water, η=80%=0.8

Mass of the aluminum beaker, m=30gm

Mass of the water, mw=250gm

Formula used:

The intensity of the transmitted wave is related to the incident wave by

I=Iocos2θ

Here,

I is the intensity of transmitted light

Io is the intensity of incident wave

θ is the angle between the direction of polarized light and the axis of polarizing filter

Calculation:

The intensity of the transmitted light is calculated as

I=Iocos2θ

Plugging the values in the above equation

I=1000cos220I=883W/m2

Since there are two polarizers, therefore the final intensity of the light will be one fourth

I=8834=220

To determine

(b)

Do the polarizing filters get hot?

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