Question

The total consumption of electrical energy in the United States is about 1.0 1019 joules per year.

Answer 1

Answer:

a) 316880878140.2895 Joules

b) 1056.26 Joules

c) 372.80103310622 km²

Explanation:

Energy consumption

$E=\frac{P}{t}\\\Rightarrow E=\frac{1\times 10^{19}}{365.25\times 24\times 60\times 60}\\\Rightarrow E=316880878140.2895\ W$

Average rate of electrical energy consumption is 316880878140.2895 Joules

Total population = 300 million

$E=\frac{316880878140.2895}{300\times 10^6}\\\Rightarrow E=1056.26\ J$

Each person consumes 1056.26 Joules.

Efficiency = 0.85

Power from Sun

$0.85\times 1000=850\ W/m^2$

Area

$\frac{316880878140.2895}{850}=372801033.10622\ m^2$

Converting to km²

$372801033.10622=\frac{372801033.10622}{1000\times 1000}=372.80103310622\ km^2$

Area required to collect the electrical energy used in the United States is 372.80103310622 km²

Answer 2

The average rate of electrical energy consumption is 316880878140.2895 Joules . The average rate of electrical energy consumption per person is 1056.26 Joules . An area 372.80103310622 km² (in square kilometers) would be required to collect the electrical energy used in the United States

Explanation:

The total consumption of electrical energy in the United States is about 1.0 *10^19 joules per year.

The formula links energy and power is:

Energy = Power x Time.

The unit of energy is the joule, whereas unit of power is the watt and the unit of time is the second.

(a) What is the average rate of electrical energy consumption?

Energy = Power x Time

Energy= 1/(10*10^19) x (365.26 x 24 x 60 x 60)

Energy = 316880878140.2895 joules

b) The population of the United States is about 300 million people. What is the average rate of electrical energy consumption per person?

Total population = 300 million

Energy = 316880878140.2895/ {300 x 10^6}

Energy =  1056.26 J

c) The sun transfers energy to the earth by radiation at a rate of approximately 1.0 kW per square meter of surface. If this energy could be collected and converted to electrical energy with 85% efficiency, how great an area (in square kilometers) would be required to collect the electrical energy used in the United States?

Efficiency = 0.85

Power from Sun = 0.85 x 1000 = 850 W/m^2

Area  = 316880878140.2895 x 850 = 372801033.10622 m^2

Converting to km²

= {372801033.10622}{1000 x 1000}

= 372.80103310622 km^2

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