Heat Radiation and Temperature – Rankers Physics

Heat Transfer - Radiation: Practice Problem & Solution

Assertion (A): Bodies radiate heat at all temperature. Reason (R): Rate of radiation of heat is proportional to the fourth power of absolute temperature.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Heat Transfer - Radiation. Understanding the underlying formula is key to arriving at the correct answer below:

All bodies above 0 K radiate thermal energy. The Stefan-Boltzmann law states that the rate of radiation P is proportional to the fourth power of absolute temperature \(T^4\), i.e., \(P \propto T^4\). This law confirms that radiation occurs at any temperature above absolute zero and quantifies it. Thus, R explains A.

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): As the temperature of the blackbody increases, the wavelength at which the spectral intensity \(E_\lambda\) is maximum decreases. Reason (R): The wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature.  
2. Assertion (A): The average translational kinetic energy of the molecules in one mole of all ideal gases, at the same temperature is the same. Reason (R): The average kinetic energy of one mole of any ideal gas at temperature T is given by \( \frac{3}{2}RT \).  
3. Assertion (A): Temperature of a rod is increased and again cooled to same initial temperature then its final length is equal to original length. Reason (R): For a small temperature change, length of a rod varies as \( l = l_0 (1+\alpha \Delta T) \) provided \( \alpha \Delta T is small  \). Here symbol have their usual meaning.  
4. Assertion (A): An ideal gas expands isothermally, during this process, it absorbs \( 25 \text{ J} \) heat. In the first law of thermodynamics, work done on the gas will be \( -25 \text{ J} \). Reason (R): There will be no change in the internal energy of the gas during isothermal expansions.  
5. For hydrogen gas $C_p - C_v = a$ and for oxygen gas $C_p - C_v = b$, so the relation between $a$ and $b$ is given by: (1991)