Wien's Law Calculator

The following are the principles and guidelines for determining an object's black body temperature.

• To determine the light's highest wavelength.
• The peak wavelength is multiplied by the Wien's displacement constant.
• Otherwise, examine the light's peak frequency.
• The body temperature is calculated by multiplying the peak frequency by the constant.

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Wien's Law, also known as Wien's Displacement Law, asserts that black body radiation has various temperature maxima at different wavelengths and that the temperatures are inversely proportional.

Wien's Law is depicted in the following way: λ_max = b/T

Here is a representation of Wien's Law with frequency.

f_max = k * T

Here,

• The peak wavelength of light is λ_max
• T be the black body's absolute body temperature.
• b = 2.8977719 mm*K is the Wien's displacement constant
• f_max be the peak frequency
• k= 5.878 * 10¹⁰ Hz/K is the numerical constant

Question 1: The wavelength of maximal solar radiation has been calculated to be around 0.52 μm. What is the temperature of the sun's surface?

Solution:

Consider the problem, we have

Maximum Wavelength = 4.75 m = 4.75 x 10^-7 m

b=2.9 x 10^-3 m K

The formula for Wien's Displacement Law is wavelength = b/Temperature.

Temperature=b/Wavelength

T = 2.9 x 10-3/4.75 x 10^-7

T= 2.9 x 10-3/4.75 x 10^-7

T= 2.9 x 10

T=6100°K

As a result, the sun's surface temperature is 6100°K.

1. What applications does Wien's displacement law have?

Wien's law is used to determine the temperatures of hot radiant objects such as stars and the sun, as well as any radiant object whose temperature is much higher than that of its surroundings. The sun's temperature and incandescent bulb light are two examples of Wien's displacement rule in action.

2. What is Wien's constant's value?

The numerical constant utilised in the peak frequency formula is k = 5.8789232*10¹⁰ Hz/K, while the Wien's law constant value is b = 2.8977719 mm*K.

3. What is the formula for calculating an object's body temperature using Wien's law?

The temperature may be calculated using two simple calculations using Wien's displacement law. The peak frequency is used in one case, whereas the peak wavelength is used in the other.

• Temperature = b/(peak_wavelength)
• Temperatute = (peak_frequency)/k

4. The human body has a temperature of 43 degrees Celsius. What wavelength has the highest intensity of radiation released by the human body?

We have,

• Human body temperature T = 43 + 273 = 316 K
• peak_wavelength = b/Temperature
• peak_wavelength= 0.002897 mK/316 K
• peak_wavelength= 9.16 x 10^-6
• Therefore, The maximum wavelength is 9.16 x 10^-6