91Ó°ÊÓ

Power: Power is a scalar quantity defined as the amount of energy consumed per unit time.

Mathematically,

\(P = \frac{E}{T}\)

Here, \(P\) is the power, \(E\) is the energy consumed or generated, \(T\) is the time.

As a result, the expression of the energy consumed is,

\(E = PT\)

A person in good physical condition can pedal bicycle at \(13 - 18{\rm{ km}}/{\rm{h}}\) for \(12{\rm{ hrs}}\) a day (\(12{\rm{ hrs}}\) of resting period is given per day). Neglecting any problems of generator efficiency. Determine the number of people it would take to replace an electric power plant that generates \(10{\rm{ MW}}\).

The energy generated by a person pedaling bicycle is,

\(E = PT\)

Here, \(P\) is the power generated by a person good physical by pedaling bicycle at \(13 - 18{\rm{ km}}/{\rm{h}}\) \(\left( {P = 400{\rm{ W}}} \right)\), and \(T\) is the time of pedaling bicycle \(\left( {T = 12{\rm{ hr}}} \right)\).

Putting all known values,

\(\begin{array}{c}E = \left( {400{\rm{ W}}} \right) \times \left( {12{\rm{ hrs}}} \right)\\ = 4800{\rm{ W}} \cdot {\rm{h}}\end{array}\)

The energy generated by electric power plant is,

\(E' = P'T'\)

Here, \(P'\) is the power generated by the electric power plant \(\left( {P' = 10{\rm{ MW}}} \right)\), and \(T'\) is the time \(\left( {T' = 1{\rm{ day}}} \right)\).

Putting all known values,

\(\begin{array}{c}E' = \left( {10{\rm{ MW}}} \right) \times \left( {1{\rm{ day}}} \right)\\ = \left( {10{\rm{ MW}}} \right) \times \left( {\frac{{{{10}^6}{\rm{ W}}}}{{1{\rm{ MW}}}}} \right) \times \left( {1{\rm{ day}}} \right) \times \left( {\frac{{24{\rm{ hrs}}}}{{1{\rm{ day}}}}} \right)\\ = 2.4 \times {10^8}{\rm{ W}} \cdot {\rm{h}}\end{array}\)

The number of people required to replace the electric power plant is,

\(N = \frac{{E'}}{E}\)

Here, \(E'\) is the energy generated by the electric power plant \(\left( {E' = 2.4 \times {{10}^8}{\rm{ W}} \cdot {\rm{h}}} \right)\) and \(E\) is the energy generated by a person by pedaling bicycle \(\left( {E = 4800{\rm{ W}} \cdot {\rm{h}}} \right)\).

Putting all known values,

\(\begin{array}{c}N = \frac{{2.4 \times {{10}^8}{\rm{ W}} \cdot {\rm{h}}}}{{4800{\rm{ W}} \cdot {\rm{h}}}}\\ = 50000\end{array}\)

Therefore, the number of people required to replace electric power plant that generates \(10{\rm{ MW}}\) is \(50000\). Hence, \(50000\) people can replace the coal or petroleum power plant which generates the same energy.