Water Temperature and Different Altitudes

[maryana-b1]

TL;DR

Comparing water at different altitudes for the same temperature

If I have a 10L vessel of water at 1800 meters at 80C, and I have an equivalent vessel at 10 meters.

If I wanted to be equivalent what would I need to heat the vessel at 10 meters to?

Would it be 80C, would it be slightly higher because of the lower pressure at 1800 meters?

 

[DaveC426913]

If I wanted to be equivalent...

Equivalent what?

Boiling point, perhaps?

This sounds like a homework question. It should be posted in the homework section. There is a template there where you supply any formulae you think are necessary.

Forum rules require you to make an effort at a solution and show your work before we can help you.

 

[Andrew Mason]

TL;DR Summary: Comparing water at different altitudes for the same temperature

If I have a 10L vessel of water at 1800 meters at 80C, and I have an equivalent vessel at 10 meters.

If I wanted to be equivalent what would I need to heat the vessel at 10 meters to?

Would it be 80C, would it be slightly higher because of the lower pressure at 1800 meters?

It is not clear what you are trying to equate. I will answer this on the assumption that you are trying to equate internal energy for the same mass of water at different external pressures.

The air pressure at 10 m above sea level would be about 101.2 kPa and at 1800 m it would be about 83.6 kPa. The boiling point of water at 83.6 kPa would be about 93.4 C, so at 80C the water would still be in liquid form.

Since water molecules have potential energy, a higher volume of the same mass of water at the same temperature would have greater internal potential energy. However, since liquid water is very close to being incompressible, hence almost inexpandable, the difference in volume between an external pressure difference from 101.2 to 83.6 kPa will be maybe a few microlitres. So internal energy would be essentially determined by temperature. You would have to bring the 10L at 10 m altitude to 80C to have the same internal energy.

AM

 

[DaveC426913]

I will answer this...

Again:

Forum rules require [posters] to make an effort at a solution and show [their] work before we can help...

 

[maryana-b1]

Hi Sorry this isn't a homework question (Been out of school a long time), this is just a question between my friends.

Let me clarify a little, at what temp does the water at 10M need to be at to be equally close to the boiling point as the water at 1800M that is at 80°C. Does that make more sense?

Here's the math I got.

The boiling point of water decreases by about 1.1°C for every 300 meters increase in altitude.

The boiling point decrease from sea level (where boiling point is 100°C) is approximately (1800/300) * 1.1°C ≈ 6°C. So the approximate boiling point at 1,864 meters is 100°C - 6°C ≈ 94°C.

10M is about sea level, We can approximate it as 100°C

The difference between the given temperature (80°C) and the boiling point at 1,864 meters:

94°C - 80°C = 14°C

and then

100°C - 14°C = 86°C

So then 80°C at 1,800 meters is roughly equivalent to 86°C at 10 meters

 

[russ_watters]

That looks right to me with the caveat that "equally close" could be read as a percentage vs a certain baseline (like relative humidity). But if you're sure of the intent, it's good.