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Q49 PE
Expert-verifiedUsing data from Table 7.5, calculate the daily energy needs of a person who sleeps for 7.00 h, walks for 2.00 h, attends classes for 4.00 h, cycles for 2.00 h, sits relaxed for 3.00 h, and studies for 6.00 h. (Studying consumes energy at the same rate as sitting in class.)
The daily energy needs of a person is \(3799.62{\rm{ kcal}}\).
Useful work: Useful work includes all the work done by a person, because these are accomplished by exerting forces (nonconservative in nature) on the outside work.
Daily energy need of a person is,
\(E = {P_{sl}} \times {T_{sl}} + {P_w} \times {T_w} + {P_{ac}} \times {T_{ac}} + {P_{cy}} \times {T_{cy}} + {P_s} \times {T_s} + {P_{st}} \times {T_{st}}\)
Here, \({P_{sl}}\) is the power consumed in sleeping \(\left( {{P_{sl}} = 83{\rm{ W}}} \right)\), \({T_{sl}}\) is the time spent in sleeping \(\left( {{T_{sl}} = 7.00{\rm{ h}}} \right)\), \({P_w}\) is the power consumed in walking \(\left( {{P_w} = 280{\rm{ W}}} \right)\), \({T_w}\) is the time spent in walking \(\left( {{T_w} = 2.00{\rm{ h}}} \right)\), \({P_{ac}}\) is the power consumed in attending classes \(\left( {{P_{ac}} = 210{\rm{ W}}} \right)\), \({T_{ac}}\) is the time spent in attending classes \(\left( {{T_{ac}} = 4.00{\rm{ h}}} \right)\), \({P_{cy}}\) is the power consumed in cycling \(\left( {{P_{cy}} = 400{\rm{ W}}} \right)\), \({T_{cy}}\) is the time spent in cycling \(\left( {{T_{cy}} = 2.00{\rm{ h}}} \right)\), \({P_s}\) is the power consumed in sitting relaxed \(\left( {{{\rm{P}}_{\rm{s}}}{\rm{ = 125 W}}} \right)\), \({T_s}\) is the time spent in sitting relaxed \(\left( {{T_s} = 3.00{\rm{ h}}} \right)\), \({P_{st}}\) is the power consumed in studying \(\left( {{P_{st}} = 210{\rm{ W}}} \right)\), and \({T_{st}}\) is the time spent in studying \(\left( {{T_{st}} = 6.00{\rm{ h}}} \right)\).
Putting all known values,
\(\begin{aligned}E &= \left( \begin{aligned}{l}\left( {83{\rm{ W}}} \right) \times \left( {7.00{\rm{ h}}} \right) + \left( {280{\rm{ W}}} \right) \times \left( {2.00{\rm{ h}}} \right) + \left( {{\rm{210 W}}} \right){\rm{ \times }}\left( {{\rm{4}}{\rm{.00 h}}} \right) + \\\left( {{\rm{400 W}}} \right) \times \left( {2.00{\rm{ h}}} \right) + \left( {125{\rm{ W}}} \right) \times \left( {3.00{\rm{ h}}} \right) + \left( {210{\rm{ W}}} \right) \times \left( {6.00{\rm{ h}}} \right)\end{aligned} \right)\\ &= 4416{\rm{ W}} \cdot {\rm{h}} \times \left( {\frac{{1{\rm{ J}}/{\rm{s}}}}{{1{\rm{ W}}}}} \right) \times \left( {\frac{{3600{\rm{ s}}}}{{1{\rm{ hr}}}}} \right)\\ &= 15897600{\rm{ J}} \times \left( {\frac{{{\rm{1 kcal}}}}{{4184{\rm{ J}}}}} \right)\\ &= 3799.62{\rm{ kcal}}\end{aligned}\)
Therefore, the required daily energy needs of a person is \(3799.62{\rm{ kcal}}\).
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