# Ideal gas formula not working?

• B
• ContrapuntoBrowniano
In summary, the water-filled pot is changing its temperature even when the pressure and volume are held constant. This phenomenon is only observed for liquids, and is due to the accumulation of energy in the liquid-steam phase change.
ContrapuntoBrowniano
TL;DR Summary
Why does pressure and volume seem unnaffected for temperature changes in a heated cooking pot filled with water?
Hi! I wanted to do some basic calculations for temperature T on a water-filled pot. I noticed something strange on my calculations, and couldn’t figure out what was wrong...
So here it is:
The ideal gas formula:
k=PV
The actual formula Relates equally the product PV with the a constant associated with temperature. So, i never saw any flaws in this relationship for fluids...until today! You’ll see... If we vary the pressure or the volume leaving the other one constant, then the temperature will also vary accordingly, however, if we vary the temperature, the pressure and volume migth stay the same! This is the case of the heated water pot:
If water is an uncompressible fluid, the pressure changes appear insignificant to it, and since the only thing i’m doing is heating water, the volume stays the same...but “T” IS rising. Is there something I’m not considering?

ContrapuntoBrowniano said:
This is the case of the heated water pot:
If water is an uncompressible fluid, the pressure changes appear insignificant to it, and since the only thing i’m doing is heating water, the volume stays the same...but “T” IS rising. Is there something I’m not considering?
Liquid water isn't a gas, so the gas laws do not apply to it.

OmCheeto, russ_watters, robphy and 3 others
Lnewqban said:
Welcome!

The water molecules are accumulating energy that will end up in the liquid-steam phase change.

https://en.wikipedia.org/wiki/Enthalpy_of_vaporization

https://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html

If you freeze up the same water pot, you could measure an expansion or increasing volume.
Ok, but that does not account for this formula not working! Thermodynamics tells that
PV and nRT both have energy units (kg*m^2*s^-2 in SI) so: in this case n stays and so does R, but again, T changes?
Enthalpy does not come anywhere near this, and even if it does, the fluid is still changing i’ts temperature even when T<100C=212F
I’ve come up with some answers, but maybe they’re wrong:
-The formula only works for constant temperature.
-It only works for gases
-Infinitesimal variations in P or R result in considerable temperature changes for uncompressible fluids.

Drakkith said:
Liquid water isn't a gas, so the gas laws do not apply to it.
That’s what i was thinking...however, this just moves the problem over to liquids.

ContrapuntoBrowniano said:
this just moves the problem over to liquids.
How? Liquids are not guesses.

ContrapuntoBrowniano said:
That’s what i was thinking...however, this just moves the problem over to liquids.
Wasn't the problem "the ideal gas law doesn't accurately describe the behavior of heating water" and the answer "liquid water isn't an ideal gas so the ideal gas law doesn't apply"? It seems to me the problem is solved.

So what problem are you referring to?

vanhees71, OmCheeto, ContrapuntoBrowniano and 1 other person
In general, it is important to know the limits of validity for any formula that you use. You cannot blindly plug in variables, you need to understand what those variables mean and when the formula applies to those variables. ##PV=nRT## applies only to ideal monoatomic gasses, and it is no longer valid when a material deviates significantly from the behavior of an ideal gas. That is the case with a liquid.

vanhees71, jbriggs444, robphy and 3 others
ContrapuntoBrowniano said:
Ok, but that does not account for this formula not working! Thermodynamics tells that
PV and nRT both have energy units (kg*m^2*s^-2 in SI) so: in this case n stays and so does R, but again, T changes?
Enthalpy does not come anywhere near this, and even if it does, the fluid is still changing i’ts temperature even when T<100C=212F
I’ve come up with some answers, but maybe they’re wrong:
-The formula only works for constant temperature.
-It only works for gases
-Infinitesimal variations in P or R result in considerable temperature changes for uncompressible fluids.
https://en.wikipedia.org/wiki/Ideal_gas_law

- Isothermal thermodynamic processes are the only ones keeping temperature constant.

- Most real gases deviate from that ideal behavior.

- Variations of pressure do not result in considerable temperature changes for uncompressible fluids; take hydraulic fluid for example.

The nature of pressure in liquids (mainly due to surrounding pressure and gravity or internal molecular potential energy) is different than the internal pressure that naturally exists for liquids forced to remain within certain volume at certain temperature (or internal molecular kinetic energy).

ContrapuntoBrowniano
So what problem are you referring to?
How? Liquids are not *gasses
I’m referring to the problem of a Thermodynamic formula for the internal energy of liquids, in terms of heat capacity, amount and temperature. Maybe there is one? Something like an analogy for liquids of the Gas law.

Lnewqban
ContrapuntoBrowniano said:
Summary: Why does pressure and volume seem unnaffected for temperature changes in a heated cooking pot filled with water?

Is there something I’m not considering?
What you are asking for is the equation of state. The ideal gas law is approximately valid for simple gases at moderate temperature and pressure. The surprise is not that is an inexact description for water but that it is as broadly applicable as it is. There are various approaches as indicated in the link.

vanhees71 and ContrapuntoBrowniano
hutchphd said:
What you are asking for is the equation of state. The ideal gas law is approximately valid for simple gases at moderate temperature and pressure. The surprise is not that is an inexact description for water but that it is as broadly applicable as it is. There are various approaches as indicated in the link.
Thanks! I’ll check it out.

ContrapuntoBrowniano said:
I’m referring to the problem of a Thermodynamic formula for the internal energy of liquids, in terms of heat capacity, amount and temperature. Maybe there is one? Something like an analogy for liquids of the Gas law.
A common approximation is to assume a constant volume process so dU=dQ. If evaporation becomes important, things get more complicated.

Lnewqban
ContrapuntoBrowniano said:
Summary: Why does pressure and volume seem unnaffected for temperature changes in a heated cooking pot filled with water?
Pressure rising along with temperature in a fixed volume is the basis of the pressure cooker. The higher pressure allows the temperature to get hotter than boiling water to cook faster.

https://scienceandsamosa.com/scienc...rks on,then pressure would naturally increase.

So, the Ideal Gas Law works fine you just have to put a lid on it!

Dale and Lnewqban
ContrapuntoBrowniano said:
... Enthalpy does not come anywhere near this, and even if it does, the fluid is still changing i’ts temperature even when T<100C=212F
Copied from
https://en.wikipedia.org/wiki/Enthalpy

"The enthalpy H of a thermodynamic system is defined as the sum of its internal energy and the product of its pressure and volume:
H = U + pV
where U is the internal energy, p is pressure, and V is the volume of the system.

...
The U term is the energy of the system, and the pV term can be interpreted as the work that would be required to "make room" for the system if the pressure of the environment remained constant. When a system, for example, n moles of a gas of volume V at pressure p and temperature T, is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy U plus pV, where pV is the work done in pushing against the ambient (atmospheric) pressure."

## 1. Why is the ideal gas formula not working for my experiment?

There could be several reasons why the ideal gas formula is not working for your experiment. It is possible that the conditions of your experiment do not match the assumptions of the ideal gas law, such as high pressures or low temperatures. Additionally, there may be experimental errors or variations in the gas sample that can affect the accuracy of the formula.

## 2. Can the ideal gas formula be used for all gases?

No, the ideal gas formula is only applicable to ideal gases, which are hypothetical gases that follow certain assumptions, such as having no intermolecular forces and occupying no volume. Real gases deviate from these assumptions, and therefore, the ideal gas law may not accurately predict their behavior.

## 3. How can I improve the accuracy of the ideal gas formula in my experiment?

To improve the accuracy of the ideal gas formula, you can try to minimize experimental errors by using precise measuring equipment and controlling the conditions of your experiment. Additionally, you can use a modified version of the ideal gas law, such as the van der Waals equation, which takes into account the deviations of real gases from ideal behavior.

## 4. What are some limitations of the ideal gas formula?

The ideal gas formula has several limitations, including the assumption that gases have no intermolecular forces and occupy no volume. It also does not take into account the effects of high pressures and low temperatures, which can cause real gases to deviate from ideal behavior. Additionally, the ideal gas law does not consider the molecular structure of gases, which can affect their behavior.

## 5. Is there an alternative to using the ideal gas formula?

Yes, there are alternative equations that can be used to describe the behavior of gases, such as the van der Waals equation, the Peng-Robinson equation, and the Redlich-Kwong equation. These equations take into account the deviations of real gases from ideal behavior and can provide more accurate results in certain conditions.

• Classical Physics
Replies
6
Views
911
• Classical Physics
Replies
2
Views
715
• Classical Physics
Replies
0
Views
613
• Classical Physics
Replies
27
Views
1K
• Classical Physics
Replies
18
Views
1K
• Classical Physics
Replies
3
Views
1K
• Classical Physics
Replies
3
Views
380
• Classical Physics
Replies
2
Views
1K
• Classical Physics
Replies
2
Views
867
• Classical Physics
Replies
7
Views
1K