Question

What will be the ratio of rate of radiation of metal sphere at two different temperatures \(T_1 = 527^{\circ}\)C and \(T_2 = 127^{\circ}\)C

• A. \(4:1\)
• B. \(16:1\)
• C. \(8:1\)
• D. \(64:1\)

Hint:

Rate of radiation is proportional to \(T^4\) (Kelvin).

Answer 1

The Correct Option is B

Step 1: Plan:
Compare the two temperatures as a ratio without computing the power.

Step 2: Steps:
The temperature in Kelvin doubles from $400$ K to $800$ K. Doubling $T$ multiplies $T^4$ by $2^4 = 16$. If one had used Celsius values by mistake, the ratio $\frac{527}{127}$ would give a completely different number.

Final Answer:
The ratio of radiation rates is $16:1$, option (B). \[ \boxed{16:1} \]