Steam tables give you properties for steam at a given pressure P and temperature T. You are told a steam sample is at P = 500 kPa and T = 151.8°C (which happens to be the saturation temperature at that pressure). What additional information do you need to fully specify the state?
ANothing — pressure and temperature always fully specify the state of a pure substance
BThe specific enthalpy h, which is always needed alongside P and T
CThe quality x (vapor mass fraction), because at saturation conditions liquid and vapor coexist
DThe density ρ, which determines whether the substance is liquid or gas at this point
At saturation conditions (T = Tₛₐₜ at that pressure), the substance is inside the two-phase dome, where liquid and vapor coexist. In the two-phase region, pressure and temperature are not independent — they both lie on the saturation curve — so specifying both still leaves the state underdetermined. You need the quality x (mass fraction vapor) to locate the state between the saturated liquid line (x = 0) and the saturated vapor line (x = 1). This is invisible on a P-T diagram but clearly shown by the saturation dome in P-v space.
Question 2 Multiple Choice
Water at 400°C is gradually compressed at constant temperature from very low pressure. Starting as a vapor, what phase does it become if pressure is raised well above 22.1 MPa (the critical pressure for water)?
AIt becomes a compressed liquid — sufficient pressure always liquefies any gas
BIt remains a supercritical fluid — above the critical temperature, no phase boundary separates liquid from gas no matter how much pressure is applied
CIt becomes a solid — sufficient pressure at high temperature always drives solidification
DIt passes through the saturation dome and emerges as liquid, just as at lower temperatures
Above the critical temperature (374°C for water), the vapor-pressure curve no longer exists — there is no liquid-gas phase boundary to cross. Compressing water above 374°C produces a supercritical fluid that transitions continuously between gas-like and liquid-like behavior with no distinct phase change. Option A describes behavior below the critical temperature; above it, you can apply any amount of pressure and no condensation (visible phase boundary) will occur.
Question 3 True / False
The triple point and the critical point both represent conditions where liquid and gas coexist in equilibrium.
TTrue
FFalse
Answer: False
The triple point is where ALL THREE phases — solid, liquid, and gas — coexist simultaneously. It is the unique P-T point where all three phase boundary curves meet. The critical point is where the distinction between liquid and gas DISAPPEARS — it is the end of the vapor-pressure curve, not a coexistence point. Above the critical point, there is no phase boundary at all, so 'coexistence' doesn't apply. These are fundamentally different phenomena.
Question 4 True / False
At the critical point of a pure substance, the specific volumes of the saturated liquid and saturated vapor become equal.
TTrue
FFalse
Answer: True
The critical point is the apex of the saturation dome in P-v space. Moving up the saturation envelope, the saturated liquid specific volume (vₗ) increases and the saturated vapor specific volume (vᵥ) decreases as pressure and temperature rise. They converge and become identical at the critical point — which is why the dome closes there. Beyond the critical point, the distinction between liquid and vapor vanishes precisely because there is no longer a difference in their properties.
Question 5 Short Answer
Why is specifying both pressure and temperature alone insufficient to determine the thermodynamic state of a substance inside the saturation dome? How is the state fully specified in that region?
Think about your answer, then reveal below.
Model answer: Inside the saturation dome, liquid and vapor coexist in equilibrium. Pressure and temperature are not independent there — once you fix one, the other is determined by the saturation curve. So stating P and T gives you the same information twice; you've only specified one independent variable, not two. To fully specify the state, you need the quality x (the mass fraction of the mixture that is vapor), which locates you between the saturated liquid line (x = 0) and the saturated vapor line (x = 1). Specific volume (or specific enthalpy or entropy) can substitute for quality, since all of these vary continuously across the two-phase region.
This is why engineers learn to first check whether a state is inside the dome before looking up properties. If you use superheated steam tables for a two-phase state, you will find no valid entry — or worse, interpolate to a nonsensical result. The P-v diagram makes this visual: the saturation dome shows exactly which states are two-phase and reminds you that volume (not just T and P) varies within it.