Question

01) As reservas reutilizáveis de petróleo na Terra correspondem a uma energia de cerca de $\sf{1,7\times 10^{22}J}$.
a) Considerando que o Sol tem uma luminosidade $\sf{L_{๏}=3,85\times 10^{33} erg/s}$, em quanto tempo a energia irradiada pelo Sol torna-se equivalente à energia das reservas de petróleo?​

Answer 1

Siga a resolução abaixo

$\sf{ t_{a}\approx \frac{E_{p}}{ L_{๏}} } \\ \\ \sf{t_{a}\approx \: \frac{(1,7 \times {10}^{22}) \times {10}^{7} }{3,85 \times {10}^{33} } } \\ \\ \sf{t_{a}\approx \: \frac{1,7 \times {10}^{22} \times {10}^{7} }{ \frac{77}{20} \times {10}^{33} } } \\ \\ \sf{t_{a}\approx \: \frac{1,7 \times {10}^{7} }{ \frac{77}{20} \times {10}^{33 - 22} } } \\ \\ \sf{t_{a}\approx \: \frac{1,7 \times {10}^{7} }{ \frac{77}{20} \times {10}^{11} } } \\ \\ \sf{t_{a}\approx \: \frac{ \frac{17}{10} \times {10}^{7} }{ \frac{77}{20} \times {10}^{11} } } \\ \\ \sf{t_{a}\approx \: \frac{ \frac{17}{10} }{ \frac{77}{20} \times {10}^{11 - 7} } } \\ \\ \sf{t_{a}\approx \: \frac{ \frac{17}{10} }{ \frac{77}{20} \times {10}^{4} } } \\ \\ \sf{t_{a}\approx \: \frac{ \frac{17}{10} }{ \frac{77 \times {10}^{4} }{20} } } \\ \\ \sf{t_{a}\approx \: \frac{17}{10} \div \frac{77 \times {10}^{4} }{20} } \\ \\ \sf{t_{a}\approx \: \frac{17}{10} \times \frac{20}{77 \times {10}^{4} } } \\ \\ \sf{t_{a}\approx \: \frac{17 \times 20}{10 \times 77 \times {10}^{4} } } \\ \\ \sf{t_{a}\approx \: \frac{17 \times 2}{77 \times {10}^{4} } } \\ \\ \sf{t_{a}\approx \: \frac{34}{77 \times {10}^{4} } } \\ \\ \sf{t_{a}\approx \: \frac{34}{77 \times 10000} } \\ \\ \sf{t_{a}\approx \: \frac{17}{77 \times 5000} } \\ \\ \sf{t_{a}\approx \: \frac{17}{385000} } \\ \\ \red{\boxed{\boxed{\sf{t_{a}\approx \: 4,41 \times {10}^{ - 5} \: \: s}}}}$

Resposta: $\sf{t_{a}\approx \: 4,41 \times {10}^{ - 5} \: \: s}$

At.te: José Armando