Question

If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor

• A. $8$
• B. $2$
• C. $4$
• D. $16$

Hint:

Always remember that radiation power depends on the fourth power of absolute temperature ($T^4$). A simple mental shortcut for these types of questions is to take the scaling multiplier (2) and raise it to the fourth power: $2^4 = 16$. If the temperature had tripled, the factor would be $3^4 = 81$!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Determine how radiated power changes when the absolute temperature of a body is scaled by a given factor.

Step 2: Key Formula or Approach:
According to the Stefan-Boltzmann Law, the power radiated per unit area is proportional to the fourth power of absolute temperature: P ∝ T⁴. For any temperature multiplier n, the power scales by n⁴.

Step 3: Detailed Explanation:
If the temperature doubles (multiplier = 2), the radiated power increases by 2⁴ = 16 times. Had the temperature tripled instead, the factor would jump to 3⁴ = 81. This exponential dependence means even modest temperature increases produce dramatic rises in radiative output. Remembering this T⁴ proportionality provides a rapid mental shortcut for any thermal radiation scaling problem.

Step 4: Final Answer:
Doubling the temperature multiplies radiated power by 16.