# Absolute air humidity in a hot motor compartments

#### fseg

Hello, I have a real-life thermodynamics problem for which I would like your help for understanding.

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 Michell Humidity Calculator). Now, I am driving my car and the temperature in the motor compartment/surroundings heats up to about 90 °C. Then my question: what is now the absolute humidity in the motor/hot region?

Although a concrete calculation/result would be greatly appreciated, ultimately I would like to understand how the equilibrium between both connected open sub-systems (cool atmosphere - hot motor compartment) is reached and what relation govern it in order to be able to perform analytical calculations.

I would assume that the total pressure of both regions, exterior and motor, is constant. Furthermore, that the partial pressures of both dry air and water vapor remain also constant. However I am not sure to what extent is this correct or I am allowed to completely treat them as ideal gases.

Thank you very much.