(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 60 kg hiker wishes to climb to the summit of Mt. Ogden , an ascent of 1500 m.

a) Assuming that she is 25 % efficient at converting chemical energy from food into mechanical work, and that essentially all the mechanical work is used to climb vertically , roughly how many bowls of corn flakes(standard serving 1 ounce, 100 kilocalories) should the hiker eat before setting out?

b) As the hiker climbs the mountain , 3-quarters of the energy from the corn flakes is converted to thermal energy. If there were no way to dissipate this energy , how many degrees would her body temeperature increase?

c) In fact, the extra energy does not warm the hiker's body significantly; instead, it goes(mostly) into evaporating water from her skin. How many liters of water should she drink during the hike to replace the lost fluids?(At 298 K, a reasonable temperature toassume , the latent heat of vaporization of water is 580 cal/g, 8 % more than at 373 K)

2. Relevant equations

mgh=U

Q=delta(T)*C

PV=RT

delta(H)=delta(U)+Pdelta(V)

3. The attempt at a solution

a) mgh=(60)(9.8)(1500) =882000 joules=882 kJ

If she works at 25 % efficiency, I should considered only .75*mgh=662 kJ

4.184 kJ=1 kilocalorie => 662 kJ=158 kilocalories==> 1 .58 ounces or 1.58 bowls of corn flakes

b) delta(H)=Q+W_other. Does no dissipation mean Q=0? If so then delta(T) = 0

c) Q=Lm=(580 cal/g)(18 g)= 10440 g; PV=RT; T=298 K, R=8.31 J/K, P=1.01e5 , why would they give me the latent heat of vaporization when I can just T, R and P to find the volume?

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# Hiker climbs top of mountain; energy conversion problem

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