If the temperature of an object is doubled, how does the rate of heat radiation

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Question: If the temperature of an object is doubled, how does the rate of heat radiation change?

Options:

Correct Answer: It quadruples

Solution:

According to the Stefan-Boltzmann law, if the temperature is doubled, the rate of heat radiation increases by a factor of 2^4 = 16.

If the temperature of an object is doubled, how does the rate of heat radiation change?

If the temperature of an object is doubled, how does the rate of heat radiation change?

Step 1: Understand that heat radiation is related to temperature.
Step 2: Learn about the Stefan-Boltzmann law, which states that the power (rate of heat radiation) emitted by an object is proportional to the fourth power of its absolute temperature.
Step 3: If the original temperature is T, and we double it, the new temperature becomes 2T.
Step 4: According to the Stefan-Boltzmann law, the rate of heat radiation at temperature T is proportional to T^4.
Step 5: Calculate the new rate of heat radiation at temperature 2T: (2T)^4 = 16T^4.
Step 6: Compare the new rate of heat radiation (16T^4) to the original rate (T^4).
Step 7: Conclude that the rate of heat radiation increases by a factor of 16 when the temperature is doubled.

Stefan-Boltzmann Law – The law states that the power radiated by a black body is proportional to the fourth power of its absolute temperature (P ∝ T^4).