[fseg2]

Hello, I have what I think will be a simple question for many of you.

Let's say today is a hot humid day, with 30 °C and 80% relative humidity, what means that the absolute humidity of air will be about 24 g/m^3 (according to http://www.michell.com/us/calculator/). Now, I am driving my car and the temperature in the motor compartment and its surroundings is about 90 °C. Then my question: how is the equilibrium of this open system determined in terms of humidity?

-Is the driving force for equilibrium the balance of relative humidity? If this would be the case, the motor compartment would be at 80% rel. hum. and 335 g/m^3 abs. hum.

-Or is it rather the balance of absolute humidity (the actual concentration of water in air) the driving force? In this case, the motor compartment would have also 24 g/m^3, meaning about 6% rel. hum.

-Any other option? Partial pressures...

For any given response, would it be also valid in a wide range of temperatures and relative humidities (-30 to 120 °C and 0 to 100% rel. hum.)?

Thank you very much

[Borek]

Or is it rather the balance of absolute humidity (the actual concentration of water in air) the driving force? In this case, the motor compartment would have also 24 g/m^3, meaning about 6% rel. hum.

That's more or less what I would expect.

Any other option? Partial pressures...

My bet is that it is more or less equivalent to the absolute humidity. When you heat the air up you don't change the composition, so as long as we treat it as an ideal gas mole fraction doesn't change. Partial pressure is mole fraction times total pressure and (if we talk about the engine compartment) heating of the air is an isobaric process.

For any given response, would it be also valid in a wide range of temperatures and relative humidities (-30 to 120 °C and 0 to 100% rel. hum.)?

Probably depends on how accurate you want to be. As long as the ideal gas approximation works (and water doesn't condense) nothing changes. That probably means several percent errors somewhere, especially when the temperature gets lower.

[fseg2]

Or is it rather the balance of absolute humidity (the actual concentration of water in air) the driving force? In this case, the motor compartment would have also 24 g/m^3, meaning about 6% rel. hum.

That's more or less what I would expect.

Hi, thanks for your input. Intuitively, I also think it goes with this line. However partial pressures have probably something to say there and the different temperatures may affect a 1:1 relationship. Any hint on how to approach this analytically? Would it be right to assume, that the partial pressures of both environmets (atmosphere and motor surroundings) should be equal? I should be able to do some simple math if that's true.

[Enthalpy]

Essentially, no process adds nor removes humidity from the air (condensation for instance would be a different situation). When the air gets hotter and can contain more humidity, the same amount of water means a smaller relative humidity.

Since air and water interact little, the maximum amount of vapour that air can contain relates closely with the partial pressure of vapour that leads to condensation, even without air.

In the described situation, the amount of vapour in the air is small, so its effect on the volume can be neglected. The effect of the temperature on the air volume is less negligible if wanting accurate answers.

I didn't expect 90°C in the air of the motor compartment. That would be a temperature for the engine's coolant circuit, and the coolant is itself cooled by air which must be less hot.

From -30°C to +120°C, you must write the equations a bit cleanly. The standard way is to write them for vapour and for air, add the volumes and the partial pressures. The total pressure equates the atmospheric one (except air flow effects) and the amount of vapour is given by previous conditions (if no condensation occurs).

[fseg2]

Thanks Enthalpy. 90°C in the motor compartment doesn't occur often, but that and even up to 120 °C are possible (extremely hot day, fast driving uphill, for instance), even more in a testing bench. I know these conditions are extreme but they are relevant for the reliability design. But for my case, 80, 70, or 200°C are the same, since I want to understand how the moisture transfer or changes. There is on one side an infinite volume of cool air with constant humidity, the atmosphere, and a small hotter volume, the motor, connected to the other.

Then, if I understood correctly, not only there is constant total pressure between ambient and hot motor area of course (~1 bar), but also the partial pressures of each gas (dry air and water vapor) should also be constant? Then, given the higher temperature there should also be an increase in volume of the hot gases. Is it the case that, in equilibrium, the extra volume of hot wet air generated is constantly removed towards the atmosphere (which acts as a giant sink) due to the natural convection and cooled by it, allowing the constant volume?

[Enthalpy]

Thanks for the motor compartment's temperature. It sounds logical that a car shall survive it, even if not permanently.

Yes, that's how I understand it. Air with its moisture are allowed to expand freely and at constant composition. And the drop in relative humidity happens because hotter air could contain more vapour than cold air.