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Q69PE

Expert-verifiedFound in: Page 555

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) A photovoltaic array of (solar cells) is 10.0% efficient in gathering solar energy and converting it to electricity. If the average intensity of sunlight on one day is 700 W/m ^{2}, what area should your array have to gather energy at the rate of 100W? (b) What is the maximum cost of the array if it must pay for itself in two years of operation averaging 10.0 hr per day? Assume that it earns money at the rate of 9.00C per kilowatt-hour.**

(a) The area needed by the array to gather energy is \({\rm{0}}{\rm{.14}}\;{{\rm{m}}^{\rm{2}}}\).

(b) The maximum cost of the array is \(657\; \not\subset \).

The given data can be listed below as:

The efficiency of the photovoltaic array of solar cells is \(e = 10.0\% = 0.1\).

The sunlight’s average intensity is \(I = 700\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\).

The rate of the energy that should be gathered is \(P = 100\;{\rm{W}}\).

The average time needed in two years is \(t = \frac{{10.0\;{\rm{hours}}}}{{{\rm{1}}\;{\rm{day}}}}\).

The rate the money is earned is \[\].

**The intensity is described as the power that is transmitted per unit area of an object. The intensity is helpful for measuring the area of a plane.**

The equation of the area is expressed as:

\(A = \frac{P}{I}\)

Here, A is the area, P is the rate of the energy that should be gathered and \(I\)is the sunlight’s average intensity.

Substitute the values in the above equation.

\(\begin{aligned}A = \frac{{{\rm{100}}\;{\rm{W}}}}{{{\rm{700}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}}}\\ = 0.14\;{{\rm{m}}^{\rm{2}}}\end{aligned}\)

Thus, the area needed by the array to gather energy is \({\rm{0}}{\rm{.14}}\;{{\rm{m}}^{\rm{2}}}\)

The equation of the total electric energy is expressed as:

\(E = ePt\)

Here, E is the total electric energy, e is the efficiency of the photovoltaic array of solar cells and t is the average time needed in two years.

Substitute the values in the above equation.

\[\begin{aligned}E = \left( {0.1} \right)\left( {100\;{\rm{W}}} \right)\left( {2\;{\rm{y}} \times \frac{{{\rm{730}}\;{\rm{day}}}}{{{\rm{2}}\;{\rm{y}}}} \times \frac{{10.0\;{\rm{hours}}}}{{{\rm{1}}\;{\rm{day}}}}} \right)\\ = \left( {10\;{\rm{W}}} \right)\left( {{\rm{730}} \times 10.0\;{\rm{hours}}} \right)\\ = \left( {10\;{\rm{W}}} \right)\left( {{\rm{7300}}\;{\rm{hours}}} \right)\\ = 73\;{\rm{kWh}}\end{aligned}\]

The equation of the maximum cost of the array is expressed as:

\({\mathop{\rm C}\nolimits} = Ec\)

Here, \({\mathop{\rm C}\nolimits} \)is the maximum cost and \(c\) is the rate the money is earned.

Substitute the values in the above equation.

\(\begin{aligned}C = \left( {73\;{\rm{kWh}}} \right) \times \left( {\frac{{9.00\; \not\subset }}{{1\;{\rm{kWh}}}}} \right)\\ = 657\; \not\subset \end{aligned}\)

Thus, the maximum cost of the array is \(657\; \not\subset \).

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