# How much time will it take to heat something up?

#### moonman239

Hey guys,

I have a question. Let's say I place a pot of water on top of a campfire. The pan is made of stainless steel. And, when placed on the ground, the pan reaches the average knee. The diameter of the pan equals the height of my chest. The thickness is negligible. The outside temperature is 65 degrees. The temperature of the water is also 65 degrees. How long will it take before I see steam coming out?

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#### berkeman

Mentor
Hey guys,

I have a question. Let's say I place a pot of water on top of a campfire. The pan is made of stainless steel. And, when placed on the ground, the pan reaches the average knee. The diameter of the pan equals the height of my chest. The thickness is negligible. The outside temperature is 65 degrees. The temperature of the water is also 65 degrees. How long will it take before I see steam coming out?
Depends. How hot is the campfire? How big? What altitude are you at?

And what is the context of the question? You going to be cooking for a small army on your next camping trip?

#### moonman239

How hot is the campfire?
As hot as your average campfire.
berkeman said:
How big? What altitude are you at?
1) As big as your average campfire 2) 512 ft.

And what is the context of the question? You going to be cooking for a small army on your next camping trip?
Nope. A Boy Scout outing, if you must know.

#### moonman239

I'll be more specific. Let's say the fire is 2,730 degrees Fahrenheit. As for how big it is, just pick a random number.

#### moonman239

Okay, let's say the fire is a circle that is 6 feet in diameter.

#### fluidistic

Gold Member
If this is a real situation rather than a homework problem (where you can depreciate the very important wind factor), I suggest you do the experiment once.
If you just want to have a very rough guess then calculate the volume of water that can enter the pan. Depreciate totally the steel and its thermal conductivity (it's much lesser than the one of water and you don't want a good accuracy).
Have a guess on the NET amount of heat entering the system (only water) per second. Calculate how much net heat income you need to raise up water from 65 degrees to the boiling degree or any other degree you like such as the steam one. You could depreciate partially at least the heat transfered from the pan to the environment if you close the pan so that the water isn't exposed to the "cold" external air. For this, you need to know the mass of water inside the pan and the thermal conductivity of water. Use the formula $$\Delta Q = mc \Delta T$$.
Then computing how many seconds you need to reach the total heat required to raise the temperature is a piece of cake.
If you want an accurate prediction, the problem becomes much harder. I'd do the experiment rather than trying to guess many data that might be totally different from the ones guessed when you're doing the experiment.

#### moonman239

@fluidistic:

Thank you for answering my question!

#### daumphys

Hey guys,

I have a question. Let's say I place a pot of water on top of a campfire. The pan is made of stainless steel. And, when placed on the ground, the pan reaches the average knee. The diameter of the pan equals the height of my chest. The thickness is negligible. The outside temperature is 65 degrees. The temperature of the water is also 65 degrees. How long will it take before I see steam coming out?
To solve this problem, you should calculate heat transfer rate.
First, you calculate the temperature of the fire.
And, calculate a total heat transfer coefficient, but this step is not easy because the system is not ideal.
And , calculate the heat capacity of the port and water.
Finally you establish heat transfer differential equations of the system.
And solve the problem. This problem is non-steady state heat transfer equation.

#### moonman239

To solve this problem, you should calculate heat transfer rate.
First, you calculate the temperature of the fire.
And, calculate a total heat transfer coefficient, but this step is not easy because the system is not ideal.
And , calculate the heat capacity of the port and water.
Finally you establish heat transfer differential equations of the system.
And solve the problem. This problem is non-steady state heat transfer equation.
My question has already been solved.

#### moonman239

@fluidistic:

If I needed to factor in wind, how would I do that?

#### fluidistic

Gold Member
@fluidistic:

If I needed to factor in wind, how would I do that?
The wind would cool down the pan so that the net heat transfer into the pan would be less than simply the heat incoming from the fire. That's why if you could close the pan the wind wouldn't affect that much, for a not very accurate result.
About what daumphys said, I think he meant "check out the heat capacity of water and the port in a book" rather than calculate. But I'm not sure his way of solving the problem would be realistic either due to the estimation rather than calculation of the net heat transfer into the system.
That's why (if it isn't homework) if you want an accurate answer, the best thing to do is to do the experiment. This is by far the best thing to do in my opinion.
Sometimes when the problem is too complex (too many unknown variables) and you have the opportunity to run the experiment for a very low cost, it's better to let the universe solve it for you. Faster and more accurate than any result you could have calculated.

#### moonman239

(if it isn't homework) if you want an accurate answer, the best thing to do is to do the experiment. This is by far the best thing to do in my opinion.
Sometimes when the problem is too complex (too many unknown variables) and you have the opportunity to run the experiment for a very low cost, it's better to let the universe solve it for you. Faster and more accurate than any result you could have calculated.
It's not homework. I actually knew there was an equation I could use. What do you mean by "unknown variables?"

#### fluidistic

Gold Member
It's not homework. I actually knew there was an equation I could use. What do you mean by "unknown variables?"
Wind speed, temperature, pressure, humidity of air for example. If you want an accurate result you'd have to take all these into accounts and probably much more. That's why I say it's better to do the experiment if you want to have an accurate result.

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