91Ó°ÊÓ

Energy consumed: Energy consumed by any device is given as the product of its power rating and the time of operation of the device.

Mathematically,

\(E = PT\)

Here, P is the power and T is the time.

The energy used in sitting relaxed and sleeping is,

\({E_u} = {P_{sitting}} \times {t_{sleep}} + {P_{sleep}} \times {t_{sleep}}\)

Here, \({P_{sitting}}\) is the power consumed in sitting relaxed \(\left( {{P_{sitting}} = 120{\rm{ W}}} \right)\), \({t_{sitting}}\) is time spent in sitting relaxed \(\left( {{t_{sitting}} = 16.0{\rm{ h}}} \right)\), \({P_{sleep}}\) is the power consumed in sleeping \(\left( {{P_{sleep}} = 83\;{\rm{W}}} \right)\), and \({T_{sleep}}\) is the time spent in sleeping \(\left( {{T_{sleep}} = 8.0{\rm{ h}}} \right)\).

Putting all known values,

\(\begin{array}{c}{E_u} = \left( {120{\rm{ W}}} \right) \times \left( {16.0{\rm{ h}}} \right) + \left( {83{\rm{ W}}} \right) \times \left( {8.0{\rm{ h}}} \right)\\ = \left( {120{\rm{ W}}} \right) \times \left( {16.0{\rm{ h}}} \right) \times \left( {\frac{{3600{\rm{ s}}}}{{1{\rm{ h}}}}} \right) + \left( {83{\rm{ W}}} \right) \times \left( {8.0{\rm{ h}}} \right) \times \left( {\frac{{3600{\rm{ s}}}}{{1{\rm{ h}}}}} \right)\\ = 9302400{\rm{ J}} \times \left( {\frac{{1{\rm{ kJ}}}}{{1000{\rm{ J}}}}} \right)\\ = 9302.4{\rm{ kJ}}\end{array}\)

The unutilized energy is,

\(E = {E_c} - {E_u}\)

Here, \({E_c}\) is the energy consumed \(\left( {{E_c} = 10000{\rm{ kJ}}} \right)\).

Putting all known values,

\(\begin{array}{c}E = \left( {10000{\rm{ kJ}}} \right) - \left( {9302.4{\rm{ kJ}}} \right)\\ = 697.6{\rm{ kJ}}\end{array}\)

The body converts unutilized \(39{\rm{ kJ}}\) of energy into \(1{\rm{ g}}\) body fat. Therefore, the fat gain is,

\(\begin{array}{c}F = \frac{{697.6{\rm{ kJ}}}}{{\left( {39{\rm{ kJ}}/{\rm{g}}} \right)}}\\ = 17.89{\rm{ g}}\end{array}\)

Therefore, the required amount of fats gained is \(17.89{\rm{ g}}\).