Question 544: Thermodynamics & KTG

Question

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be

Accepted Answer

$$E = \sigma A{T^4};\,\,A \propto {R^2}$$
$$	herefore$$ $$E \propto {R^2}{T^4}$$
$$	herefore$$ $${{{E_2}} \over {{E_1}}} = {{R_2^2T_2^4} \over {R_1^2T_1^4}}$$
$$ \Rightarrow {{{E_2}} \over {{E_1}}}$$
$$ = {{{{\left( {2R} ight)}^2}{{\left( {2T} ight)}^4}} \over {{R^2}{T^4}}}$$
$$ = 64$$

Answer

$$32$$

Answer

$$16$$

Answer

$$4$$

Answer

$$64$$

Thermodynamics & KTG

If the temperature of the sun were to increase from $T to 2T and its radius from R to 2R$, then the ratio of the radiant energy received on earth to what it was previously will be

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