Phase transitions

Water in a pot zWater in a pot: some molecules escape since by accident they got enough energy to escape the attraction from the other water molecules zRate of escape x determined by temperature (and surface area) zConversely, T determined by x given the surface area

Four questions  A lid is first placed on top of the water surface and then lifted a small distance, so that some evaporation can take place. This is done isothermally. W,  U kin,  U, Q is a) positive b) zero c) negative

Water in a pot II zx molecules leave the surface per second zThey bang against lid and walls (pressure) zIn equilibrium, x molecules per second return zDetermines the pressure of vapour and liquid

Water in a pot III zNow lift the lid a bit further, isothermally zSame T so same x zBriefly, less molecules return as they travel further zEquilibrium: more molecules in vapour phase, again x molecules return per second zSame momentum per molecule so same pressure

Water in a pot IV zLikewise, if we lift the lid isobarically we can show that the process must be isothermal zThis is the same as heating a pot of water on the stove without a lid! zHence water has a boiling point (at 100 °C)

Comments zThe heat needed to boil 1 kg of a substance is called the latent heat of vaporisation L vap zDuring the phase transition the temperature remains constant zHence

Enthalpy  From First Law: L =  U + p  V  p is constant: L =  U +pV) zQuantity H = U +pV is called enthalpy  L =  H for isobaric phase transitions

p,V-diagram: an isotherm p vapour V LIQUIDLIQUID + VAPOUR VAPOUR p

Question zAt higher pressure, boiling occurs at a) higher temperature b) the same temperature c) lower temperature

p,V-diagram: isotherms pcpc V p LIQUID FLUID T = T c T < T c LIQUID+VAPOUR VcVc critical point

p,T diagram pressure temperature critical point triple point p+ p p  LIQUID VAPOUR SOLID FLUID

The Clausius-Clapeyron equation zGives an equation for the slope of the p,T- curves zStandard derivations use differential calculus zThermodynamics allows us to use simple algebra

A Gedanken Carnot engine zImagine a piece of matter about to melt yWe’re on the fusion curve at p+  p, T+  T. zAdd heat until molten. yisobaric & isothermal zExpand adiabatically to p, T zRemove heat isothermally until fully solidified zAdiabatic compression to starting point

p,V diagram V solid V liquid p+ p p  Exaggerated: liquid nearly incompressible

Efficiency zRemember: for any Carnot engine: zW   p·(V liquid -V solid ); Q H = L fusion ; T H = T +  T  T zSubstitute:

General form zTake the limit  T  0 and generalise for any phase transition: zThis is the Clausius-Clapeyron equation

Definitions zIf a gas consists of more than one component, each constituent gas can be thought to exert a partial pressure zExample: air at 1 atmosphere: p nitrogen  0.8 atm, p oxygen  0.2 atm. zVapour pressure: pressure of vapour phase in equilibrium with the solid/liquid phase

Dew point zRelative humidity (for water):  Start  <100%. p vap decreases with decreasing T zAmount of water in air constant: p vap becomes equal to p partial zT lower: condensation until p vap = p partial again

PS225 – Thermal Physics topics zThe atomic hypothesisThe atomic hypothesis zHeat and heat transferHeat and heat transfer zKinetic theoryKinetic theory zThe Boltzmann factorThe Boltzmann factor zThe First Law of ThermodynamicsThe First Law of Thermodynamics zSpecific HeatSpecific Heat zEntropyEntropy zHeat enginesHeat engines zPhase transitionsPhase transitions