Water is at 250°C and a pressure of 10 MPa. The saturation temperature at 10 MPa is approximately 311°C. What is the state of the water?
ASuperheated vapor, because 250°C is a high temperature
BSubcooled (compressed) liquid, because T < T_sat(P)
CA saturated mixture, because 250°C far exceeds the familiar boiling point of 100°C
DSuperheated vapor, because the pressure is very high
State identification requires comparing T with T_sat at the given pressure, not with 100°C (which is only T_sat at 1 atm). At 10 MPa, T_sat ≈ 311°C. Since 250°C < 311°C, the water is below its boiling point at that pressure — subcooled (compressed) liquid. This is counterintuitive: water at 250°C feels 'hot,' but at 10 MPa it is liquid, compressed below its phase boundary. The 100°C reference is only correct at atmospheric pressure.
Question 2 Multiple Choice
Steam at 400°C and 1 atm (T_sat at 1 atm = 100°C) should be described using which property table?
AThe saturated liquid table at 400°C
BThe saturated vapor table at 1 atm
CThe superheated vapor table at 400°C and 1 atm
DThe compressed liquid table at 400°C and 1 atm
Since T = 400°C > T_sat(1 atm) = 100°C, the steam is superheated. Superheated vapor properties are tabulated as functions of both T and P in the superheated vapor table. The saturated vapor table (option B) applies only to vapor exactly on the saturation curve (at T_sat), not to superheated conditions. The compressed liquid table applies to subcooled liquids, not vapors. This three-way discrimination — subcooled / saturated / superheated — determines which table to use in every thermodynamic property lookup.
Question 3 True / False
A substance is known to be on the saturation curve. Specifying its pressure alone mostly determines its thermodynamic state.
TTrue
FFalse
Answer: False
On the saturation curve, pressure and temperature are coupled — fixing one fixes the other. But this only locates the substance on the saturation boundary; it does not pin down where between saturated liquid and saturated vapor the state lies. To fully specify the state, you must also provide quality x = m_vapor / m_total (ranging from 0 for saturated liquid to 1 for saturated vapor). Without quality, two substances at the same saturation pressure can have wildly different specific volumes and enthalpies. By contrast, in single-phase regions (subcooled or superheated), pressure and temperature independently determine the state.
Question 4 True / False
The specific volume of a subcooled liquid is best approximated by the saturated liquid value at the same temperature, not the same pressure.
TTrue
FFalse
Answer: True
Because liquids are nearly incompressible, their intensive properties change little with pressure but do change meaningfully with temperature. The saturated liquid table at temperature T provides the baseline, and the small pressure correction is usually negligible. Using the saturated liquid value at the same *pressure* instead would introduce a larger error by referencing T_sat(P) — which may differ significantly from the actual subcooled liquid temperature — as the interpolation anchor. The temperature-based approximation is standard engineering practice and is explicitly justified by the incompressibility of liquids.
Question 5 Short Answer
You are told that steam is at 250°C, but not told its pressure. Can you determine whether it is subcooled liquid, on the saturation curve, or superheated vapor? Explain.
Think about your answer, then reveal below.
Model answer: No — temperature alone is insufficient to determine phase state. Whether a substance at 250°C is subcooled, saturated, or superheated depends on its pressure. At 1 atm (T_sat = 100°C), 250°C steam is superheated. At 10 MPa (T_sat ≈ 311°C), a substance at 250°C is subcooled liquid. At the saturation pressure corresponding to 250°C (about 3.97 MPa), the substance is exactly on the saturation curve. The state is determined by comparing T to T_sat(P), which requires knowing P.
This illustrates the two-property rule: for a pure substance in a single-phase region, any two independent intensive properties completely specify the state. In single-phase regions, T and P are independent — both are needed. On the saturation curve, T and P are dependent (knowing one fixes the other), but quality x is then needed as the second property to specify the state within the two-phase region. Temperature alone is always half the information required.