the sun releases 3.85×10²⁶ joules of energy every second. according to the e.i.a., the u.s. consumed about…

the sun releases 3.85×10²⁶ joules of energy every second. according to the e.i.a., the u.s. consumed about 1.03×10²⁰ joules of energy in 2011. if the u.s. continues at that rate of consumption, how many years could one second of energy from the sun power the u.s.?

the sun releases 3.85×10²⁶ joules of energy every second. according to the e.i.a., the u.s. consumed about 1.03×10²⁰ joules of energy in 2011. if the u.s. continues at that rate of consumption, how many years could one second of energy from the sun power the u.s.?

Answer

Explanation:

Step1: Calculate the number of seconds of U.S. energy - consumption

We divide the energy released by the sun in one - second by the U.S. annual energy consumption. Let $E_{sun}=3.85\times 10^{26}$ J (sun's one - second energy release) and $E_{US}=1.03\times 10^{20}$ J (U.S. annual energy consumption). The number of years $n$ is given by the ratio of the sun's one - second energy to the U.S. annual energy consumption. First, calculate the number of seconds of U.S. energy consumption from the sun's one - second energy: $\frac{E_{sun}}{E_{US}}=\frac{3.85\times 10^{26}}{1.03\times 10^{20}}$. Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{3.85}{1.03}\times10^{26-20}\approx3.74\times 10^{6}$ seconds.

Step2: Convert seconds to years

We know that there are $365\times24\times3600 = 31536000=3.1536\times 10^{7}$ seconds in a year. To convert the number of seconds to years, we divide the number of seconds by the number of seconds in a year. Let $t$ be the number of years, then $t=\frac{3.74\times 10^{6}}{3.1536\times 10^{7}}$. Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we get $t=\frac{3.74}{3.1536}\times10^{6 - 7}\approx0.119\times10^{-1}= 0.0119$ years.

Answer:

$0.0119$ years