Thermodynamics: Are pressure and temperature enough to calculate enthalpy? 
From the chart above, it looks like it is possible to calculate enthalpy from just pressure and temperature.  After a few hours of Googling my question, I'm not able to find anything helpful.
My company is interested in finding the effectiveness of an air conditioning system by measuring the change in enthalpy from one side to the other.  As a software person, I need a formula that I can use to calculate the enthalpy.  I know this formula would need to include different properties of the gas, can you elaborate on what those constants are?  Thank you very much.
 A: The formula that you are looking for is
$$H=H_0+
\int_0^\rho \frac{[P-T(\frac{\partial P}{\partial T})_{\rho}]}{\rho^2} d\rho + 
\frac{P}{\rho} -
RT + 
\frac52R(T-T_0)
$$
But this is useless to you unless you know the equation of state of your substance (if you have vapor and liquid, it is not $Pv=RT$) and the reference value $H_0$ which is attained at $T_0$. In the formula above $T$ is temperature, $P$ is pressure, $\rho$ is density (the equation of state is a relationship among these three parameters, so only two of them are independent) and $R$ is 8.31 J/mol K - the universal gas constant. 
Pressure and temperature are sufficient to compute any state variable, including enthalpy, provided you have a single chemical component (for example pure water, or pure nitrogen, or pure gold) and a single phase (gas only or liquid only or solid only, i.e. no boiling, melting, etc.) system. Moreover, for ideal gas (the kind where $Pv=RT$) temperature alone determines enthalpy (in the formula above all the terms with $P$ in them will drop out in this case), i.e. $H$ is pressure-independent. But if you have more than one component or more than one phase (the case in the diagram shown), you need to specify chemical and/or phase make-up of your system to fix the thermodynamics.
A: This is a refrigeration thermodynamic question (I say this if you wish to further look information in the web/books). It's been some years since I dealt with HVAC. But taking my trusty "Fundamentals of Engineering Thermodynamics" by Moran & Shapiro book (good reference if you're going to do this kind of stuff for a while), I'll try to shed some light. But I suggest you get a copy of a thermo book if this is going to be for a job - it's more thorough than what I'm going to write.
If you are dealing with a vapor-compression cycle (which most likely it is since this is the common air conditioning sytem), the coefficient of performance of a vapor-compression refrigeration cycle is:
$$\beta = \frac{h_1-h_4}{h_2-h_1}$$
If you are dealing with a gas refrigeration system (this is used to reach very low temperatures and specialized applications such as aircraft cooling), the coefficient of performance of the Brayton refrigeration cycle is:
$$\beta = \frac{h_1-h_4}{(h_2-h_1)-(h_3-h_4)}$$
Where $h_n$ is enthalpy at point $n$. Be careful of the location for $n$, it might change depending the source. In this case, I'm using your locations for $n$. The coefficient of performance is:
$$\beta = Q_{in}/W_{cycle}$$
Where (for a refrigeration & heat pump cycle):
$$W_{cycle} = Q_{out} - Q_{in}$$
Where "$Q_{in}$ is the energy transferred by heat into the system undergoing the cycle from the cold body, and $Q_{out}$ is the energy discharged by heat transfer from the system to the hot body." Moran & Shapiro
How to calculate enthalpy values: These values are available for the different commercially available refrigerants. If you know your refrigerant, try a web search for them or if not send a email/call to a supplier. And yes you only need pressure and temperature. They are usually found either by tables, or Pressure-Enthalpy diagrams (which look very scary for the untrained eye, but you get a hold of them pretty quickly):
http://www2.dupont.com/Refrigerants/en_US/assets/downloads/h47122_SuvaHP_push.pdf
To answer your question directly:
The "effectiveness of an air conditioning system" is usually measured by the coefficient of performance. And yes, it can be calculated by using just enthalpy values. But with all four values of the refrigeration cycle, not just two like I think you are asking.
Values you need for making a calculations:
Most likely, you don't have the pressure and temperature of all points in the diagram. If you assume ideal vapor-compression refrigeration cycle, you only need:


*

*Temperature of "Cold Region (place you're keeping cool)" and "Warm Region (place you're transferring the heat to)"

*Temperature of saturated [refrigerant] vapor that enters the compressor

*Temperature of saturated [refrigerant] liquid leaving the condenser

*Refrigerant type


In the Moran & Shapiro book there are examples how to do this, and also with modifications for when there are irreversible heat transfer effects and for "actual" vapor-compression cycles. If you don't find any online, maybe I'll add the examples when I have some more free time.
A: This website from NIST: http://webbook.nist.gov/chemistry/fluid/ will give you any thermodynamic property you want for any temperature and pressure, for a range of fluids including Ethane, 1,1,1,2-tetrafluoro- (R134a).  It will even plot a graph if you like. 
If you want to put this in software you can buy the NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) code from NIST http://www.nist.gov/srd/nist23.cfm.
