Questions: Saturated and Superheated Property Regions and Tables

Question 1

A student is given steam at T = 150°C and P = 200 kPa. The saturation temperature at 200 kPa is 120.2°C. The student opens the saturated temperature tables at 150°C to find specific enthalpy. What error is being made?

• A. No error — the saturated temperature tables at 150°C give the correct properties for this state
• B. The student should use saturated pressure tables instead of saturated temperature tables
• C. Since T (150°C) > T_sat (120.2°C) at the given pressure, the state is superheated — saturated tables do not apply and superheated tables must be used
• D. The student needs to first calculate quality x before looking up any properties

Answer: (C)

The critical first step is the orientation step: compare the given temperature to T_sat at the given pressure. Since T = 150°C exceeds T_sat = 120.2°C at P = 200 kPa, the state is outside the two-phase dome in the superheated region. Saturated property tables only give values on the saturation curve itself (at the saturated liquid and saturated vapor lines). To find properties of superheated steam, you must use superheated steam tables indexed by both pressure (200 kPa) and temperature (150°C). Using saturated tables at 150°C would give properties at a different pressure entirely, producing wrong answers.

Question 2

Steam in the two-phase region has a quality of x = 0.6. Which statement correctly interprets this value?

• A. 60% of the volume is occupied by vapor and 40% by liquid
• B. 60% of the mass is vapor and 40% is liquid
• C. 60% of the heat has been added; 40% remains before reaching saturated vapor
• D. The liquid fraction is 0.6; quality measures the liquid content

Answer: (B)

Quality x is defined as m_vapor / m_total — it is the mass fraction of vapor in the two-phase mixture, also called the 'dryness fraction.' x = 0 is 100% saturated liquid; x = 1 is 100% saturated vapor. Quality does NOT measure volume fraction (vapor occupies far more volume per unit mass than liquid, so a mixture with x = 0.6 by mass has much more than 60% of its volume as vapor). The common misconception is that quality measures liquid fraction; it measures vapor fraction.

Question 3

Inside the two-phase dome, you can independently specify both temperature and pressure to fully define the thermodynamic state of the mixture.

• T. True
• F. False

Answer: False

Inside the two-phase dome, a pure substance has only one degree of freedom (Gibbs phase rule: F = C − P + 2 = 1 − 2 + 2 = 1). This means that fixing pressure automatically fixes temperature (and vice versa) — they are locked together on the saturation curve. To fully define the state inside the dome, you need pressure (or equivalently temperature) plus a second property that locates you within the dome, such as quality x, specific volume v, or specific enthalpy h. Specifying only T and P inside the dome is redundant and leaves the state underdefined.

Question 4

Superheated vapor at a given pressure has higher specific enthalpy than saturated vapor at the same pressure.

• T. True
• F. False

Answer: True

Saturated vapor (x = 1) is on the boundary of the two-phase dome — it is at T_sat for that pressure. Superheated vapor has had additional heat added beyond this point, raising its temperature above T_sat. Since enthalpy increases with temperature in a single-phase region (h increases with T at constant P), superheated vapor at any temperature above T_sat will have higher specific enthalpy than saturated vapor at the same pressure. This is the energy that makes superheated steam more useful in power cycles — it carries more energy available for work.

Question 5

Before looking up any property value in steam tables, you must determine which thermodynamic region a state is in. What is the procedure, and why does it matter?

Model answer: The procedure: given temperature T and pressure P, look up T_sat(P) from the saturation tables. If T > T_sat(P) → state is superheated; use superheated tables with both P and T as inputs. If T = T_sat(P) → state is on the saturation curve; need a second property (quality, v, u, or h) to locate it within the dome. If T < T_sat(P) → state is a compressed (subcooled) liquid. Alternatively, given T and specific volume v: compare v to v_f(T) and v_g(T) from saturated temperature tables; if v_f < v < v_g, the state is two-phase with x = (v − v_f)/v_fg. It matters because different regions require different equations and different tables: two-phase states use the quality lever-rule formula y = y_f + x·y_fg, while superheated states require table lookup at specific (P, T) with interpolation. Using the wrong table gives completely wrong property values.

This orientation step is where most thermodynamics calculation errors originate. Students who skip it and jump directly to a table produce nonsense answers because they are reading values that don't correspond to the actual physical state of the substance. The procedure is the direct consequence of the Gibbs phase rule: inside the dome (two phases), one degree of freedom; outside (one phase), two degrees of freedom — which is exactly why different input combinations and different tables are required.