# How much heat is needed to boil water on a camp stove?

• toothpaste666
In summary, the Pacific Crest Trail is a long hiking trail that requires careful estimation of fuel for hikers. A camp stove with a heat output of 700 J/s and fuel consumption of 0.15ℓ/h is typically used. To bring 5ℓ of water to boiling temperature starting from 10◦C, it would take 2691 seconds. To melt 5 kg of ice starting from -5◦C, it would take 2454 seconds. If the stove is used to boil 5ℓ of water for 10 minutes, 0.19 kg of water would be vaporized.
toothpaste666

## Homework Statement

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 0.15ℓ/h of fuel.

A)If the initial water temperature is 10◦C, how much time is required to bring 5ℓ 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 5ℓ of water for 10 min, how much water is vaporized?

dQ = mcdT

## The Attempt at a Solution

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 doesn't 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
it came out negative so no water would end up being vaporized? this is the part I am not so sure I did correctly

toothpaste666 said:
the problem doesn't give a starting temp so i will assume 10 C
It doesn't say 'bring to the boil and boil for 10 minutes', so I think you should take it to be already at the boil at the start of the 10 mins.

I thought that at first but then i thought i was wrong because wouldn't the set up be
Q = mL
but i already have Q and they give us 5liters which means m = 5kg and we know L also

toothpaste666 said:
I thought that at first but then i thought i was wrong because wouldn't the set up be
Q = mL
Depends what you mean by m. You wrote, correctly:
toothpaste666 said:
Q = mc deltaT + xL
All I'm saying is deltaT =0.

toothpaste666
oh wow. they slipped that 5 liters in there as an almost red herring.
Q = xL
420000 J= x (22.6E5 J/kg)
x = .19 kg
thank you

## 1. What is camp stove calorimetry?

Camp stove calorimetry is a method used to measure the energy content of a fuel source, typically used for camping stoves. It involves burning a known amount of fuel and measuring the heat produced to determine the energy output of the fuel.

## 2. How is camp stove calorimetry performed?

To perform camp stove calorimetry, a known amount of fuel is placed in a chamber and ignited. The heat produced is then measured using a thermometer or other heat-measuring device. The amount of fuel burned and the resulting temperature change can be used to calculate the energy content of the fuel.

## 3. What types of fuels can be used in camp stove calorimetry?

Any type of fuel that can be burned can be used in camp stove calorimetry, including propane, butane, isobutane, and other liquid or gaseous fuels. Solid fuels such as wood or charcoal can also be used, but may require some modifications to the setup.

## 4. What are the advantages of using camp stove calorimetry?

Camp stove calorimetry is a relatively simple and inexpensive method for measuring the energy content of a fuel source. It can also be performed in the field, making it a convenient option for outdoor enthusiasts and scientists conducting research in remote locations.

## 5. Are there any limitations to camp stove calorimetry?

While camp stove calorimetry can provide a good estimate of the energy content of a fuel, it may not be completely accurate due to factors such as incomplete combustion or energy lost to the surrounding environment. It is also limited to measuring the energy content of liquid or gaseous fuels, and may not be suitable for solid fuels or specialized fuels such as ethanol.

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