Question

Wavelength corresponding to the maximum energy is inversely proportional to the absolute temperature is known as ______

• A. Kirchhoff's law
• B. Stefan Boltzman law
• C. Wein's displacement law
• D. Raoult's law

Hint:

Remember the value of Wein's constant as \( 2898 \text{ }\mu\text{m}\cdot\text{K} \).
This allows you to quickly calculate the peak wavelength of radiation emitted by bodies like the sun (\( T \approx 5800 \text{ K} \)) or the earth (\( T \approx 300 \text{ K} \)).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify the radiation heat transfer law that states that the wavelength corresponding to the maximum spectral emissive power is inversely proportional to the absolute temperature.
This is a core topic in thermal radiation.

Step 2: Key Formula or Approach:
According to Planck's distribution of radiation, blackbody spectral emissive power varies with wavelength.
The wavelength at which the spectral emissive power is maximum, \( \lambda_{\text{max}} \), is given by Wein's displacement law:
\[ \lambda_{\text{max}} \cdot T = C_w \]
where \( T \) is the absolute temperature in Kelvin, and \( C_w \) is Wein's displacement constant (\( \approx 2898 \text{ }\mu\text{m}\cdot\text{K} \)).

Step 3: Detailed Explanation:

• Wein's Displacement Law: As the temperature of a blackbody increases, the total radiated energy increases and the peak of the emissive curve shifts to shorter (more energetic) wavelengths.
This explains why objects heated to high temperatures first glow red, then yellow, and eventually white or blue.
Mathematically, the relationship is:
\[ \lambda_{\text{max}} \propto \frac{1}{T} \]

• Stefan-Boltzmann Law: States that the total energy radiated per unit surface area of a blackbody per unit time is directly proportional to the fourth power of its absolute temperature:
\[ E_b = \sigma \cdot T^4 \]

• Kirchhoff's Law: States that for a body in thermal equilibrium, its emissivity is equal to its absorptivity:
\[ \epsilon = \alpha \]

• Raoult's Law: Describes vapor-liquid equilibrium and is unrelated to radiation heat transfer.


Step 4: Final Answer:
The relationship where the peak wavelength is inversely proportional to temperature is known as Wein's displacement law.