Chapter 37, Problem 1CQ

To determine

If the radiated intensity shift towards shorter wavelengths, towards longer wavelengths, or remain the same.

Answer to Problem 1CQ

Solution:

Shift towards longer wavelengths.

Explanation of Solution

Given:

The following data is given

A brass plate at room temperature radiates 10 W of blackbody radiation.

The plate is cooled to $-30°C$

Formula used:

The wavelength corresponding to the peak of the intensity graph is given by

${\lambda }_{peak}(\text{in }nm\text{) =}\frac{2.90\times {10}^6\text{ nm K}}{T}$

Where;

T = the temperature of the body in kelvin.

Calculation:

The wavelength corresponding to the peak of the intensity graph is

${\lambda }_{peak}(\text{in }nm\text{) =}\frac{2.90\times {10}^6\text{ nm K}}{T}$

From the equation, it is clear that the wavelength corresponding to peak of intensity is inversely proportional to the temperature.

Hence, as the temperature increases, the wavelength corresponding to maximum intensity decreases. That is, wavelength shifts towards lower value of wavelengths. But when the temperature decreases the wavelength of the maximum intensity increases. That is the radiated intensity shifts towards longer wavelengths.

Therefore, when the brass plate is cooled to $-30°C$, the radiated intensity shifts towards the longer wavelengths.

Conclusion:

The radiated intensity shifts towards the longer wavelengths.