Question

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Bodies radiate heat at all temperatures
Reason R: Rate of radiation of heat is proportional to the fourth power of absolute temperature
In light of the above statements, choose the correct answer from the options given below:

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

To determine if R is the correct explanation for A, read the assertion, add "because," and then read the reason.
"Bodies radiate heat at all temperatures because the rate of radiation is proportional to the fourth power of temperature."
This statement does not flow logically, confirming that R is not the cause of A.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero.
The fundamental nature of this emission is described by thermodynamic principles and the Stefan-Boltzmann law.

Step 2: Detailed Explanation:
Let us analyze both the Assertion and the Reason individually:
- Assertion A: According to Prevost's Theory of Heat Exchanges, all bodies at all temperatures above absolute zero (\( 0 \text{ K} \)) continuously emit thermal radiation to their surroundings.
At the same time, they also absorb radiation from other bodies.
The continuous molecular and atomic vibrations within any substance at a non-zero temperature cause the emission of electromagnetic energy.
Therefore, Assertion A is true.
- Reason R: According to the Stefan-Boltzmann law, the total rate of thermal radiation emitted per unit surface area of a blackbody is directly proportional to the fourth power of its absolute temperature:
\[ E_b = \sigma T^4 \]
where \( \sigma \) is the Stefan-Boltzmann constant and \( T \) is the absolute temperature in Kelvin.
Therefore, Reason R is also true.
- Evaluating the Connection: Although both statements are individually true, the fourth-power mathematical relationship described in Reason R does not explain why bodies emit radiation at all temperatures.
The fundamental explanation for Assertion A is that molecular motion occurs at all temperatures above absolute zero.
The Stefan-Boltzmann law simply quantifies the rate of this radiation as a function of temperature.
Therefore, R is not the correct explanation of A.

Step 3: Final Answer:
Both A and R are true but R is NOT the correct explanation of A.