91Ó°ÊÓ

The efficiency is the ratio of the total useful output by the total input. It is a measure of how efficiently a device uses energy.

Mathematically,

\(\eta \% = \frac{{{P_o}}}{{{P_i}}} \times 100\% \)

Here, \(\eta \) is the efficiency, \({P_o}\) is the useful power output, and \(P\) is the total power input.

The total power input of the person can be calculated using equation (1.1).

Rearranging equation (1.1) in order to get an expression for the total power input.

\({P_i} = \frac{{{P_o}}}{{\eta \% }} \times 100\% \)

Here,\({P_o}\)is the useful power output\(\left( {{P_o} = 350{\rm{ W}}} \right)\), and\(\eta \)is the efficiency of cycling\(\left( {\eta = 20\% } \right)\).

Putting all known values,

\(\begin{aligned} {P_i} &= \frac{{\left( {350{\rm{ W}}} \right)}}{{20\% }} \times 100\% \\ &= 1750{\rm{ W}}\end{aligned}\)

The energy consumed is,

\(E = {P_i}t\)

Here,\({P_i}\)is the input power\(\left( {{P_i} = 1750{\rm{ W}}} \right)\), and t is the time of operation\(\left( {t = 234{\rm{ min}}} \right)\).

Putting all known values,

\(\begin{aligned} E &= \left( {1750{\rm{ W}}} \right) \times \left( {234{\rm{ min}}} \right)\\ &= \left( {1750{\rm{ W}}} \right) \times \left( {234{\rm{ min}}} \right) \times \left( {\frac{{60{\rm{ sec}}}}{{1{\rm{ min}}}}} \right)\\ &= 24570000{\rm{ J}} \times \left( {\frac{{1{\rm{ kcal}}}}{{4184{\rm{ J}}}}} \right)\\ &= 5872.37{\rm{ kcal}}\end{aligned}\)

Therefore, the required energy used in metabolism during flight is \(5872.37{\rm{ kcal}}\).