Question

Each square metre of sun’s surface radiates energy at the rate of $6.27\times {10}^{7}W{m}^{-2}$. Assuming that Stefan’s law applies to the radiation, the temperature of sun’s surface is (Stefan’s constant $\sigma =5.7\times {10}^{7}W{m}^{-2}{K}^{-4}$)

• A. $(1.1\times {10}^{15})K$
• B. $(1.1\times {10}^{15}{)}^{\frac{1}{2}}K$
• C. $(1.1\times {10}^{15}{)}^{\frac{1}{3}}K$
• D. $(1.1\times {10}^{15}{)}^{\frac{1}{4}}K$

Answer 1

The correct option is D

$(1.1\times {10}^{15}{)}^{\frac{1}{4}}K$

From Stefan’s law $Q=\sigma T^4$

$\therefore T={\left(\frac{Q}{\sigma }\right)}^{\frac{1}{4}}={\left(\frac{6.27\times {10}^7}{5.7\times {10}^{-8}}\right)}^{\frac{1}{4}}=(1.1\times {10}^{15}{)}^{\frac{1}{4}}K$

Hence the correct choice is (d).