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The left line of the dome shows the saturated liquid (hf) line which separates the liquid from vapor-liquid phase. The right line shows the saturated vapor (hg) phase which separates the vapor phase from vapor-liquid phase. There are areas with constant pressure that can be shown by isobars and as they pass through the vapor-liquid phase, they are horizontal. That means while the liquid is vaporizing, both temperature and pressure do not change.
OK now, first off, we need to know the different phases of substances we are dealing with in thermodynamics:
Solid does not take the shape of its container
Fluids take the shape of their container, which can be categorized into liquids and gases but,
Saturated liquid (hf) is a liquid that has absorbed as much energy as it can but has not vaporized yet (e.g. liquid water at its boiling point 100oC or 212oF).
Subcooled liquid is the liquid which is not at its boiling point.
Liquid-Vapor mixture is two-phase of the mixture of the same substance in liquid and gas form.
Perfect gas is an ideal gas with constant specific heats.
Saturated vapor (hg) is a vapor right at the verge of condensing into a liquid form. (that is why it rains!)
Superheated vapor is the gas with more energy absorbed than only to vaporize it from liquid from.
Ideal gas is a highly supreheated vapor and there is a law for it, which we will get to later (very low pressure or temperature much higher than critical temperature, otherwise the substance is in vapor form)
Real gas is the outlaw gas that does not behave according to the ideal gas laws.
Gas mixture constitutes two or more gases freely mingling together.
Vapor-gas mixture is the mix of gases and vapor such as what we breathe called atmospheric air.
A substance's properties can be determined by three properties of pressure, temperature, and specific volume. They create a 3D graph named P-T-V diagram. If one of these properties are held constant, a 2D graph can be generated as a projection of the P-T-V diagram, which is called equilibrium or phase diagram. The most important part of this diagram is a bell-shaped curve called vapor dome that shows the liquid-vapor region. What is nice for this dome is that its vertical axis can take temperature or pressure and its horizontal axis can take specific volume, internal energy, enthalpy, or entropy, and all the principle relationships still apply. Inside the vapor dome, the parameter called quality is the fraction of vapor mass to the total mass. This property can be so helpful in finding many other properties if the state is in the vapor dome.
So, each substance has some properties that can be used to determine the thermodynamic states of the substance:
Intensive properties are independent of the amount of substance or its mass (e.g. temperature, pressure, stress)
extensive properties are dependent on the mass of substance (e.g. volume, strain, charge, mass)
Mass (kg or lbm) of a substance is independent of location or gravitational field. Pressure is shown as lbf/in2 or Pa (N/m2). In solving thermodynamic problems, absolute pressure (disregarding the atmospheric pressure) is used. Temperature depends on the energy content in the substance (heat energy). If two objects are in thermal equilibrium, no heat energy flows between them, as it normally flows from a hot to a cold object. If several objects are in thermal equilibrium that means they are all in the same temperature, which is known as the Zeroth Law of Thermodynamics. Remember always use absolute temperature (kelvin in SI and rankine in US system) is used, which is independent of substance properties.
Specific volume (ft3/lbm, m3/kg) is the volume per unit of mass (inverse of specific mass). Sum of all types of energy in a substance excluding pressure, potential, and kinetic energy results in internal energy, U, (British thermal unit, Btu, or Joule, J), which is a function of temperature. Specific internal energy, u = U/m, is shown by Btu/lbm or J/kg. The total useful energy of a substance is called enthalpy, H = U + PV, which consists of internal energy and flow energy (aka, flow work, p-V work). Specific enthalpy is h = u + Pv = H/m. Specific heat or heat capacity (c) of a substance is the amount of heat energy, Q, that is required to increase the temperature of the mass of substance by one unit: c = Q/m∆T. Heat capacity for constant volume and constant pressure are denoted by cv and cp. The ration of these two is called k = cp/cv. For FE exam, these values are given in tables so can be used for calculations.
Entropy (S), is the energy that cannot be used for work, or the disorder (randomness) in the system. According to the third law of thermodynamics (also known as Nernst theorem), the absolute entropy becomes zero only in temperature of absolute zero (Lim (s) --> 0, when temperature approaches 0). When entropy increases, it is known as entropy production, and the total entropy in a system is the summation of all its entropy productions through its lifetime. Similar to the other properties, specific entropy is entropy per unit mass (s = S/m).
Gibb's function for a pure substance that is used for latent heat changes and chemical reactions represents free energy within a system as G = H - TS = U + pV - TS, or in terms of specific parameters as g = h - Ts = u + pv - Ts. Another function used for chemical reactions is the Helmholtz free energy: A = U - TS = H - pV - TS, or a = u - Ts = h - pv - Ts. These two functions are explained nicely in this page (accessed 9/14/2015).
An equation of state shows the relationship between the state properties (volume, temperature, pressure, etc.). According to Avogadro's law, different gases with the same volume, temperature, and pressure, have the same number of molecules. Avogadro's number, NA = 6.022 x 1023 is the number of molecules in 1 gram-mole of an ideal gas. Therefore, for 1 mole of any gas, Avogadro's law can be represented as an equation of state for an ideal gas: pV = ṜT, where Ṝ is the universal gas constant. Therefore, the quantity pV/T is always constant for an ideal gas, no matter what process it undergoes. Now, if we have more than 1 mole (n moles) of ideal gas then pV = nṜT, where n = m/MW is mass divided by molecular weight. If we combine these equations we will have: pV = m(Ṝ/MW)T = mRT, where R is called specific gas constant with a molecular weight of MW. This equation can be written in terms of specific volume (divided by mass) as pv = RT.
The specific gas constant for an ideal gas is related to its specific heat values: R = cp - cv. In an ideal gas, the changes in enthalpy, entropy, and internal energy do not depend on the type of process the gas undergoes and there are equations related to those properties in thermodynamics. If in a process happens in constant entropy it is called isentropic process.
We also need to know about the speed of sound, c equals to square root of kRT, where k is the ration of specific heats in constant pressure and constant volume. Mach's number is the ratio of speed of the substance to speed of sound M = v/c.
There is another interesting point called triple-point, where all three phases of solid, liquid, and gas can coexist at the same time. If in the vapor dome diagram, the vertical axis is changed to pressure and horizontal axis changed to enthalpy, still everything is the same but we will have lines of constant temperature called isotherms and their slopes are different than isobars.
Right on top of the bell shape curve of vapor dome, we have a critical point that suddenly separates the liquid-vapor phase from the gas phase. This point helps to distinguish gas from vapor. The isobar that passes through this point is also called critical isobar. So, on the right side of the vapor dome, below the critical isobar we have vapor and above it we have gas.
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