Question

If ambient temperature is 300 K, the rate of cooling at 600 K is H. In the same surroundings, the rate of cooling at 900 K is

• A. \( \frac{16}{3} H \)
• B. \( 2H \)
• C. \( 3H \)
• D. \( \frac{1}{4} H \)

Hint:

Use the Stefan-Boltzmann law to relate the rate of cooling to the temperature. The difference in the fourth power of temperatures gives the rate of cooling.

Answer 1

The Correct Option is A

According to the Stefan-Boltzmann law, the rate of cooling is proportional to the fourth power of the temperature difference: \[ \text{Rate of cooling} \propto (T^4 - T_{\text{ambient}}^4) \] Let the rate of cooling at 600 K be \( H \). Then, we can write: \[ H \propto (600^4 - 300^4) \] Now, the rate of cooling at 900 K is: \[ \text{Rate of cooling at 900 K} \propto (900^4 - 300^4) \] Using the ratios, we can solve for the rate of cooling at 900 K: \[ \frac{900^4 - 300^4}{600^4 - 300^4} = \frac{16}{3} \] Thus, the rate of cooling at 900 K is \( \frac{16}{3} H \).