Thermodynamics: Phases and their transition, Lecture notes of Thermodynamics

Download Thermodynamics: Phases and their transition and more Lecture notes Thermodynamics in PDF only on Docsity! Phases and their transition We loosely understand that a substance can have different phases like solid, liquid and gas or vapor. We typically employ state variables like p, V , T for its description. In gas or vapor phase, for instance, we use equation of state such as pV = RT or (p + a/V 2) · (V − b) = RT etc. These equations are valid over a restricted range of p, V , T . We plot here water’s T − V diagram (isobars) and p − V diagram (isotherms) over a wide range of p,T ,V for different values of p and T respectively. We get the following, Phase change processes of water : Keep pressure constant at 1 kPa, the standard atmospheric pressure – the lower most line in T − V diagram. I At low T and V , we get compressed or subcooled water, expanding only slightly as T increases. I When T = 100oC, water exists as a liquid that is about to vaporize (saturated liquid). I At T = 100oC, as more heat is transferred, the saturated water starts vaporizing, saturated liquid-vapor mixture – boiling. I T remains constant at 100oC until all the water is vaporized, saturated vapor – a vapor that is about to condense. I T of pure vapor continue to rise and we get superheated vapor. As the pressure increases, the saturated liquid line and vapor line come closer and the saturated liquid-vapor mixture phase gets shorter until the point at which it vanishes i.e. the saturated liquid and vapor states become identical – no distinction between liquid and vapor phase. This specific point is called critical point. Tc = 374.14 o C, pc = 22.06MPa = 217.7 atm, Vc = 0.0032 m 3/kg I Start with ice at p = 100 KPa and add heat to it. Water temperature will rise until T = Tsat ≈ 0o C when ice begins to melt and T remains constant till all the ice is melted. I After all ice has melted, if we continued to add heat, water temperature rises and we boil the water at T = Tsat ≈ 100o C. Again, T remains constant until all the water has boiled to vapor. I With increasing p, the above process will repeat till p = pc . I Have we started at p < 0.61 KPa, ice goes sublimates to vapor. I Triple point – ice heated isobarically can go to either water or vapor. Solid, liquid and vapor coexist here. I Critical point – liquid and vapor have equal densities and distinction between vapor and liquid is almost non-existence. This is associated with the phenomenon of critical opalescence. I There is no critical point for solid-liquid transition. I Melting / fusion curve of water has negative slope – ice melts under increasing temperature, water expands on freezing. I A line on p − T diagram is called phase boundary, across which phase transition takes place. Nature of phase transition Ehrenfest classification : lowest derivative of free energy w.r.t. to some thermodynamic variable that is discontinuous at the transition. In thermal equilibrium, p and T are constant throughout the system, Gibbs free energy G is at minimum dG = 0 leading to G1 = G2. First order phase transition : co-existing phases 1. Condition of co-existence of phases µ1(T , p) = µ2(T , p) 2. First derivative of G is discontinuous across phase boundary. 3. Volume and entropy are discontinuous across phase boundary V = ( ∂G ∂p ) T and S = − ( ∂G ∂T ) p 4. CP of mixture of two phases during phase transition is infinite CP = T ( ∂S ∂T ) p → ∞, and so is β = 1 V ( ∂V ∂T ) p → ∞ Since co-existing phases have different entropies, system must absorb or release heat during phase transition – latent heat L ≡ H = T ∆S at const. pressure