This means there is an additional constraint for a liquid-vapor mixture, in addition to the equation of state. The consequence is that we only need to specify one variable to determine the state of the system. For example, if we specify Then P is set. In summary, for two phases in equilibrium P=P(T). If both phases are present, any quasi-static process at constant T is also at constant P Let us examine the pressure-volume behavior of a liquid-vapor system at constant temperatu For a single-phase perfect gas we know that the curve would be Pv=constant. For the two-phase system the curve looks quite different, as indicated in Figure 2B-2 D Critical point Mixture of口 iquid and口 LIquid saturation curve curve Volume v Figure 2B-2-P-v diagram for two-phase system showing isotherms can coexist. This is roughly dome-shaped and is thus often referred to as the"vapor dome,"por Several features of the figure should be noted. First, there is a region in which liquid and vapor Outside of this regime, the equilibrium state will be a single phase. The regions of the diagram in which the system will be in the liquid and vapor phases respectively are indicated. Second is th steepness of the isotherms in the liquid phase, due to the small compressibility of most liquids Third, the behavior of isotherms at temperatures below the"critical point"(see below )in the region to the right of the vapor dome approach those of an ideal gas as the pressure decreases and the ideal gas relation is a good approximation in this region The behavior shown is found for all the isotherms that go through the vapor dome. At a high enough temperature, specifically at a temperature corresponding to the pressure at the peak of the vapor dome, there is no transition from liquid to vapor and the fluid goes continuously from a liquid-like behavior to a gas-type behavior. This behavior is unfamiliar, mainly because the temperatures and pressures are not ones that we typically experience; for water the critical temperature is 374C and the associated critical pressure is 220 atmospheres2B-2 This means there is an additional constraint for a liquid-vapor mixture, in addition to the equation of state. The consequence is that we only need to specify one variable to determine the state of the system. For example, if we specify T then P is set. In summary, for two phases in equilibrium, P PT = ( ). If both phases are present, any quasi-static process at constant T is also at constant P. Let us examine the pressure-volume behavior of a liquid-vapor system at constant temperature. For a single-phase perfect gas we know that the curve would be Pv = constant. For the two-phase system the curve looks quite different, as indicated in Figure 2B-2. Volume, V Pressure, P Liquid phase Mixture of￾ liquid and￾ vapor Liquid saturation curve Vapor saturation￾ curve Critical point Vapor phase Gas phase Critical isotherm D B A C Figure 2B-2 – P-v diagram for two-phase system showing isotherms Several features of the figure should be noted. First, there is a region in which liquid and vapor can coexist. This is roughly dome-shaped and is thus often referred to as the “vapor dome”. Outside of this regime, the equilibrium state will be a single phase. The regions of the diagram in which the system will be in the liquid and vapor phases respectively are indicated. Second is the steepness of the isotherms in the liquid phase, due to the small compressibility of most liquids. Third, the behavior of isotherms at temperatures below the “critical point” (see below) in the region to the right of the vapor dome approach those of an ideal gas as the pressure decreases and the ideal gas relation is a good approximation in this region. The behavior shown is found for all the isotherms that go through the vapor dome. At a high enough temperature, specifically at a temperature corresponding to the pressure at the peak of the vapor dome, there is no transition from liquid to vapor and the fluid goes continuously from a liquid-like behavior to a gas-type behavior. This behavior is unfamiliar, mainly because the temperatures and pressures are not ones that we typically experience; for water the critical temperature is 374o C and the associated critical pressure is 220 atmospheres