The Pacific Crest Trail stretches from Mexico to Canada through the mountains of

Question

The Pacific Crest Trail stretches from Mexico to Canada through the mountains of California, Oregon and Washington. Hikers on this trail must carefully estimate the amount of fuel they will need. They will typically carry a small camp stove which produces 700 J/s of heat (this is heat added to the food, extra heat is needed to heat the pan, stove, air, and ground, but we will ignore that) and which burns 0.15 l/h of fuel.

(a) If the initial water temperature is 10 C, how much time is required to bring 5 l of water to boiling temperature?

(b) How much time will be required to melt 5 kg of ice which has an initial temperature of -5 C? The final temperature will be 0 C.

(c) Water found in mountain streams is often boiled for 10 min to make sure that it is safe to drink. If the camp stove is used to boil 5 l of water for 10 min, how much water is vaporized?

Explanation / Answer

A) first i want 5 liters of water in kg

5 liters = 5E-3 m^3

d = m/v d for water = 1000kg/m^3

1000 = m /5E-3

m = .005(1000) = 5 kg

now use Q = mcdeltaT to find heat needed

where c the specific heat of water = 4186 J/kgC and the boiling temp of water = 100C

Q = mcdeltaT = (5kg) (4186 J/kgC) (100 C- 10 C) = 1883700 J

the stove burns 700J/s so

1883700J (s/700 J) = 2691 s to bring the water to boiling temp

B) heat of fusion of water/ice = 3.33E5 J/kg = L

specific heat of ice 2100 J/kgC

we need the heat to bring the water to 0C + heat to melt water

mcdeltaT + mL

5kg(2100 J/kgC) (0 - (-5 C)) + 5kg (3.33E5 J/kg) = 5(2100)(5)J + 5(3.33E5)J = 1717500 J

which takes 1717500 J (s/700 J) = 2454 s

C) 10 min = 600 s. stove burns 700 J/s

so (700 J/s)(600 s) = 420000 J of heat are used

heat of vaporization for water L = 22.6E5 J/kg

the problem doesnt give a starting temp so i will assume 10 C

the stove will bring the water to 100C and then will vaporize some of it

let m be the total mass of water and let x be mass vaporized

Q = mcdeltaT + xL

420000 J = (5kg)(4186 J/kgC)(100 C -10 C) + x(22.6E5 J/kg)

420000 J = 1883700 J + x(22.6E5 J/kg)

-14636700 J = x (22.6E5 J/kg)

x = 65 kg

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