# Example Problem with Complete Solution

2C-2 : State of a System at a Given Temperature and Pressure 4 pts
 Ammonia exists in a sealed tank at each of the following temperatures and pressures. In each case, what phase or phases could exist in the system? Show your work and explain your reasoning. a.) 25oC, 114.7 kPa b.) -31.59oC, 50 kPa c.) -18.85oC, 200 kPa d.) -37.41oC, 100 kPa Read : At these temperatures and pressures, it is safe to assume that no solid water, or ice, exists in the system.  So, the question becomes whether the system contains superheated vapor or subcooled liquid or whether the system is in VLE.  If the system is in VLE, then P = P*(T).  Another way to look at this is that T = Tsat(P).  At saturation, it is not possible to determine the quality of the system without knowing the value of another intensive variable, such as v, u or h.  So, we are not able to state whether both vapor and liquid exist, but we can say that both could exist under these conditions.  Fortunately, that is exactly what we are asked to determine in this problem. Given: Part a.) T 25 oC P 114.7 kPa Part b.) T -31.59 oC P 50 kPa Part c.) T -18.85 oC P 200 kPa Part d.) T -37.41 oC P 100 kPa Find: What phase or phases could exist in the system? Explain. Assumptions: 1- No solid water, or ice, exists in the system. Equations / Data / Solve: In each part  of this problem, we need to determine the saturation temperature associated with the system pressure.  Then we can compare the actual system temperature to the saturation temperature. If : Tsys > Tsat Then : The system contains a superheated vapor. If : Tsys < Tsat Then : The system contains a subcooled liquid. If : Tsys = Tsat Then : The system could contain an equilibrium mixture of saturated liquid and saturated vapor. This is not always the easiest approach and for this part of the problem, there is an easier approach. Another way to solve this problem is to determine the vapor pressure of water at the actual system temperature.  We can then compare the actual system pressure to the vapor pressure at Tsys. If : Psys < P*(Tsys) Then : The system contains a superheated vapor. If : Psys > P*(Tsys) Then : The system contains a subcooled liquid. If : Psys = P*(Tsys) Then : The system could contain an equilibrium mixture of saturated liquid and saturated vapor. Part a.) The second method is easier for part (a) because Tsys = 25oC is listed in the Saturated Temperature Table while Psys = 114.7 kPa is not listed in the Saturation Pressure Table.  So, let's use the 2nd method ! From the Saturation Temperature Table of the Ammonia Tables : P*(25oC) 1003.2 kPa Since Psys < P*(Tsys), we conclude : The system contains superheated ammonia vapor. Part b.) In this part of the problem, it is easier to use method 1, described in part (a), because Psys appears in the saturation tables, while Tsys does not. From the Saturation Pressure Table of the Ammonia Tables : Tsat(50 kPa) -46.52 oC Since Tsys > Tsat(Psys), we conclude : The system contains superheated ammonia vapor. Part c.) In this part of the problem, it is easier to use method 1, described in part (a), because Psys appears in the saturation tables, while Tsys does not. From the Saturation Pressure Table of the Steam Tables : Tsat(200 kPa) -18.85 oC Since Tsys = Tsat(Psys), we conclude : The system could contain an equilibrium mixture of saturated liquid and saturated vapor. Part d.) In this part of the problem, it is easier to use method 1, described in part a, because Psys appears in the saturation tables, while Tsys does not. From the Saturation Pressure Table of the Ammonia Tables : Tsat(100 kPa) -33.59 oC Since Tsys < Tsat(Psys), we conclude : The system contains subcooled liquid ammonia. Verify: Since all of the temperature and pressure combination in this problm appear in the ammonia tables for vapor-liquid equilibrium, no solid ammonia, or ammonia ice, is present in any of the four systems considered. Answers : Part a.) Superheated vapor. Part c.) Saturated mixture. Part b.) Superheated vapor. Part d.) Subcooled liquid. 