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Chapter 7: Q50 PE (page 263)

What is the efficiency of a subject on a treadmill who puts out work at the rate of 100 W while consuming oxygen at the rate of 2.00 L/min? (Hint: See Table 7.5.)

Short Answer

Expert verified

The efficiency of subject on treadmill is \(14.3\% \).

Step by step solution

01

Efficiency

Efficiency is defined as the ratio of useful output by the total input.

\(\eta \% = \frac{{{\rm{Useful output}}}}{{{\rm{Total input}}}} \times 100\% \)

Here, \(\eta \) is the efficiency of the system.

02

Efficiency of a subject on a treadmill

The efficiency of subject on treadmill is,

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

Here,\({P_w}\)is the power at which work is done\(\left( {{P_w} = 100} \right)\), and\({P_i}\)is input power while consuming oxygen at the rate of\(2.00{\rm{ L}}/{\rm{min}}\)\(\left( {{P_i} = 700{\rm{ W}}} \right)\).

Putting all known values,

\(\begin{aligned}\eta \% &= \frac{{100{\rm{ W}}}}{{700{\rm{ W}}}} \times 100\% \\ \approx 14.3\% \end{aligned}\)

Therefore, the required efficiency of subject on treadmill is \(14.3\% \).

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(a) Calculate the power per square meter reaching Earth鈥檚 upper atmosphere from the Sun. (Take the power output of the Sun to be\(4.00 \times {10^{26}}{\rm{ W}}\).)

(b) Part of this is absorbed and reflected by the atmosphere, so that a maximum of\(1.30{\rm{ kW}}/{{\rm{m}}^2}\)reaches Earth鈥檚 surface. Calculate the area in\({\rm{k}}{{\rm{m}}^2}\)of solar energy collectors needed to replace an electric power plant that generates\(750{\rm{ MW}}\)if the collectors convert an average of\(2.00\% \)of the maximum power into electricity. (This small conversion efficiency is due to the devices themselves, and the fact that the sun is directly overhead only briefly.) With the same assumptions, what area would be needed to meet the United States鈥� energy needs\(\left( {1.05 \times {{10}^{20}}{\rm{ J}}} \right)\)? Australia鈥檚 energy needs\(\left( {5.4 \times {{10}^{18}}{\rm{ J}}} \right)\)? China鈥檚 energy needs\(\left( {6.3 \times {{10}^{19}}{\rm{ J}}} \right)\)? (These energy consumption values are from 2006.)

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