physics concepts concerning gases and thermodynamicsReading time:
An ideal gas satisfies the requirements of the Mariotte law (in an isothermal conversion, the product of the volume by the pressure is a constant) and of the Gay Lussac law (in a constant volume, the pressure of an ideal gas will be proportional to the absolute temperature).
This law applies to ideal gas combinations: «pressure, internal energy, enthalpy and entropy of a combination of ideal gases will be respectively equal to the sum of the partial pressures, partial internal energies, partial enthalpies and partial entropies that the individual gases would have if each alone occupied the total volume at the temperature of the combined gases», i.e. :
This relation links the molar mass M of a gas expressed in g·mol–1 to its density d in relation to air under normal pressure and temperature conditions.
By definition, the specific heat is the quotient of heat capacity by mass, the heat capacity being the quantity of heat dQ that has to be supplied to a system in order to raise the temperature by 1 °C.
In gases, we have specific heat at constant pressure cp and specific heat at constant volume cv.
The specific heat cp, at constant pressure for some gases in kJ/kg·°C at 0 °C and at 760 mm of mercury (table 85) :
saturating of saturated vapour
Vapour in the presence of the generating liquid phase; this vapour is termed dry when it does not contain the slightest droplet of water.
Vapour enthalpy: this is the total quantity of heat required to convert 1 kg of water taken at 0 °C into saturated vapour at a temperature of t °C. It is the sum of the heat used to heat water from 0 to t °C (water enthalpy) and of the vaporisation heat at t °C equivalent to the necessary energy that has to be provided to convert 1 kg of water into 1 kg of vapour at t °C.
As an initial approximation and for temperatures of between 30 and 190 °C, apply the Regnault formula that provides the enthalpy on the basis of the temperature expressed in °C :
- in kJ·kg–12 538 + 1.276 t;
- in kcal·kg–1606.5 + 0.305 t.
Vapour containing droplets of water, identified by its titer x: mass of vapour expressed in kg contained in 1 kg of the mixture.
Vapour having a temperature that is higher than that of the saturating vapour at the pressure concerned. As an initial approximation, it behaves like an ideal gas.
Superheated vapour enthalpy can be calculated using the following formula :
- in kJ·kg–1 2 538 + 1.276 t + cp (t – t1);
- in kcal·kg–1 606.5 + 0.305 t + cp (t – t1).
t – t1 being the difference in temperature between saturated vapour and superheated vapour at a constant pressure. As an initial approximation, we can use cp = 2.1 kJ·kg–1. In particular, this formula can be used to estimate the enthalpy of water that is evaporated in an incineration furnace from which the gases are discharged at a temperature t, in this case t1 being equal to 100 °C.
water vapor diagram
Temperature of an unsaturated wet gas measured using a dry bulb thermometer (normal meaning of temperature).
Temperature of a wet gas that becomes saturated when in contact with a liquid film.
Temperature at which the vapour contained in the gas begins to condense through cooling at a given temperature.
saturating vapour pressure
Partial pressure of vapour in a gas at dew point.
Ratio between the partial pressure of the water vapour in the gas at the saturating vapour pressure equivalent to this gas’s dry temperature. It is usually expressed as a %.
water vapour content of a gas (m)
also called «specific or absolute humidity». If P is the total pressure for a gas having a molar mass M and partial vapour pressure pv, the water content m of a gas expressed in kg·kg–1 of dry gas, is provided by :
Thus, for air that is humidity saturated at 20 °C and at normal atmospheric pressure P = 1.013 bar; pv = 0.023 bar; m = 0.0147 kg·kg–1.
wet gas enthalpy
Heat in mixtures can be regarded as negligible, the enthalpy for a wet gas will be equal to the sum of the enthalpies for the wet gas and of the vapour.
For air, the enthalpy is provided by the following formulae :
Figure 39 of chapter flue gas treatment types provides humid air enthalpy values based on the temperature and water content of that air.