2013-2-27 p-v-T Surface For pure,simple compressible systems,pressure can be determined as a function of temperature and specific volume p=p(T,v) The graph of this relation for water is indicated by the p-v-T surface shown y Single-phase regions on the surface include solid,liquid,and vapor. Two-phase regions are located between single-phase regions,where two phases exist in equilibrium:liquid. vapor,solid-vapor,solid-liquid. 313 p-v-T Surface The dome-shaped region composed of the two-phase liquid-vapor states is called the vapor dome. A state at which a phase change begins or ends is called a saturation state.Lines bordering the vapor dome are called the saturated liquid and saturated vapor lines. At the top of the dome,where saturated liquid and saturated vapor lines meet,is the critical point. Critical temperature(T)is the maximum temperature at which liquid and vapor phases can coexist in equilibrium. Critical pressure(p)pressure at critical point. 314 7
2013-2-27 7 ►For pure, simple compressible systems, pressure can be determined as a function of temperature and specific volume: p = p(T, v) The graph of this relation for water is indicated by the p-v-T surface shown Æ ►Single-phase regions on the surface include solid, liquid, and vapor. p-v-T Surface ►Two-phase regions are located between single-phase regions, where two phases exist in equilibrium: liquidvapor, solid-vapor, solid-liquid. 3-13 p-v-T Surface ►The dome-shaped region composed of the two-phase liquid-vapor states is called the vapor dome. ►A state at which a phase change begins or ends is called a saturation state. Lines bordering the vapor dome are called the saturated liquid and saturated vapor lines. ►At the top of the dome, where saturated liquid and saturated vapor lines meet, is the critical point. ►Critical temperature (Tc) is the maximum temperature at which liquid and vapor phases can coexist in equilibrium. ►Critical pressure (pc) pressure at critical point. 3-14
2013-2-27 Projections of the p-v-T Surface p-T projection (phase diagram) p-v projection (p-v diagram) 3-15 Projections of the p-v-T Surface Projection of the p-v-T surface onto the pressure-temperature Twoduce toies plane is a phase diagram. Saturation temperature designates the temperature at which a phase change Critica takes place at a given Solid Liquid poin pressure. L Saturation pressure Vapor designates the pressure at Triple poi which a phase change takes Temperature place at a given temperature. Within two-phase regions pressure and temperature are not independent. 3-16 8
2013-2-27 8 3-15 Projections of the p-v-T Surface p-T projection (phase diagram) p-v projection (p-v diagram) Projections of the p-v-T Surface ►Projection of the p-v-T surface onto the pressure-temperature plane is a phase diagram. ►Saturation temperature designates the temperature at which a phase change takes place at a given pressure. ►Saturation pressure designates the pressure at which a phase change takes place at a given temperature. ►Within two-phase regions pressure and temperature are not independent. 3-16 Two-phase regions reduce to lines
2013-2-27 Phase Diagram (p-T) Substances that expand and contract on freezing differ in the slope of the melting line LIQUID Triple point VAPOR 3-17 Substance Behavior on Freezing Expands Contracts on freezing (H2O) on freezing 3-18 9
2013-2-27 9 Phase Diagram (p-T) 3-17 Substances that expand and contract on freezing differ in the slope of the melting line Substance Behavior on Freezing 3-18 Expands on freezing (H2O) Contracts on freezing
2013-2-27 Substance Behavior on Freezing P-v-T surface of a P-v-T surface of a substance that expands substance that on freezing(like water). contracts on freezing. Projections of the p-v-T Surface Projection of the p-v-T surface onto the pressure- specific volume plane results in a p-o diagram MPa (204 Specifie volum Isobars Projection of the p-v-T Liguid-vapoe surface onto the temperature-specific c212 volume plane results in a T-o diagram. 3-20 10
2013-2-27 10 P-v-T surface of a substance that contracts on freezing. Substance Behavior on Freezing P-v-T surface of a substance that expands on freezing (like water). 3-19 Projections of the p-v-T Surface ►Projection of the p-v-T surface onto the pressurespecific volume plane results in a p-v diagram. ►Projection of the p-v-T surface onto the temperature-specific volume plane results in a T-v diagram. 3-20 Isotherms Isobars
2013-2-27 Phase Change-Liquid States Consider a closed system consisting of a unit mass (1Kg or 1lbs)of liquid water at 20C contained within a piston-cvlinder assembly This state is represented by I(highlighted by the blue dot). Liquid states such as this,where temperature is lower than the saturation temperature corresponding to the pressure at the state.are called compressed liquid states (or subcooled liquid.or just liquid) Unit mass of liquid at 20°C (68F)→ 3-21 Saturated Liquid As the system is heated at constant pressure,the temperature increases considerably while the specific volume increases slightly. Eventually,the system is brought to the state represented by f(highlighted by the blue dot) This is the saturated liquid state corresponding to the specified pressure =220丹MP%(3204n 0h/ O MP 0YC212 Liquid wate .22 1
2013-2-27 11 ●l Phase Change – Liquid States ►Consider a closed system consisting of a unit mass (1Kg or 1lbs) of liquid water at 20oC contained within a piston-cylinder assembly. ►This state is represented by l (highlighted by the blue dot). ►Liquid states such as this, where temperature is lower than the saturation temperature corresponding to the pressure at the state, are called compressed liquid states (or subcooled liquid, or just liquid). 3-21 Unit mass of liquid at 20°C (68F)Æ Saturated Liquid ● f 3-22 ►As the system is heated at constant pressure, the temperature increases considerably while the specific volume increases slightly. ►Eventually, the system is brought to the state represented by f (highlighted by the blue dot). ►This is the saturated liquid state corresponding to the specified pressure