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Clausius – Clapeyron Equation

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Clausius – Clapeyron Equation CLAUSIUS – CLAPEYRON EQUATION UG Course CLAUSIUS – CLAPEYRON equation can be used to explain the relationship between equilibrium transition temperature and pressure during the phase transition of any substance. Learning Goals • Interpret the effect of changes in pressure on equilibrium transition temperatures. • Calculate the changes in equilibrium transition temperatures given the relevant thermodynamic parameters and values. • Develop an understanding of the shape of phase boundaries as well as certain day to day phenomena using Clausius-Clapeyron equation as the basis. Author: Shrey Singh Kartikay Agarwal 10D110010 10D110030 UG sophomore year UG sophomore year Dept. of ME & MS Dept. of ME & MS Mentor: Prof. M. P. Gururajan Dept. of ME & MS DEFINITIONS AND KEYWORDS • EQUILIBRIUM TEMPERATURE(Teq) – The temperature at which phase transition takes place in a substance at certain external pressure. • GIBBS FREE ENERGY (G) = H - TS • ENTHALPY ( H )= U +PV • ENTROPY(S)- • INTERNAL ENERGY (U)- • Temperature T • Pressure P • Volume V Master Layout 1 WHY ? The above diagram shows 2 containers, one is the pressure cooker and other is an open vessel. Slide 5 and 6 Demo Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Why ? Instructions/ Working area Credits Step 1: Why? Description of the action Audio narration Text to be displayed Show the above picture on You must have observed that cooking the same the screen and then the food in an open vessel requires more time and audio narration. heat than cooking it in a pressure . cooker…..Have you ever wondered why? Step 2: Lets Answer Why? Description of the action Audio narration Text to be displayed The following text appears After going through this learning Same as the audio on the screen and the text is aid, you will be able to answer narration highlighted corresponding WHY ….. to the audio narration Cooking is faster in pressure cooker Espresso coffee tastes better than normal coffee Skiing is possible on hard ice even in temperatures much less than 0℃ . And many such different day to day examples... Master Layout 2 Getting Into the Equation The above figure shows a test tube or a vessel into which the experiment is carried out. The green part at the bottom is the liquid, the bubbles in green color are the vapours and the grey part covering the tube is the movable piston. Hence, label the figure accordingly. Slide 9, 10 and 11 Demo Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Getting into the Equation Instructions/ Working area Credits Step 1: Getting into the Equation Description of the action Audio narration Text to be displayed Show the above picture on Let us consider a generalised case of a the screen and show the weightless movable piston(weightless is bubbles moving in the tube considered so as to neglect gravity) on a closed upwards. tube . The tube is filled with a certain amount a substance(let’s say S) with surrounding temperature T1 and pressure P1 .Now if P1 is 1atm ,then the substance will boil at its normal boiling point and melt at its normal melting point but as soon as P1 is varied, the boiling point or melting point will vary accordingly. Step 2: Getting into the Equation Description of the action Audio Text to be displayed narration Show the same picture as The substance will stay in following equilibrium on the previous slide S (1) ↔ S (2) For any process dG = VdP – SdT For equilibrium conditions dG = 0 So VdP = SdT [G is the Gibbs free energy, S is entropy , (P1,T1) and (P2,T2) are the ] Integrating both the sides 푃2 푇2 힓푉. 푑푃 = 힓푆. 푑푇 푃1 푇1 푑푃 힓푆 Hence = 푑푇 힓푇 힓퐻 Also 힓S = 푇 푑푃 힓퐻 So = [CLAUSIUS-CLAPEYRON EQN.] 푑푇 힓푉.푇 (힓H is average of two phases) Step 3: Getting into the Equation Descriptio Audio Text to be displayed n of the action Show the For liquid-gas transition same picture on 힓V ≈ Vg the screen 푛푅푇 Vg = 푃 푑푃 힓퐻 So = 푑푇 푛푅푇2 [n is the number of moles, R is the universal gas constant and Vg Is the volume of gas. ] Integrating both the sides 푃2 힓퐻 1 1 ln = ( − ) 푃1 푅 푇1 푇2 Here 힓퐻 is Latent Heat Of vapourization of 1 mole Now simialr case is with melting Just 힓퐻 will be Latent Heat of fusion of 1 mole Master Layout 3 Got It Finally The above is the graphical explanation of the Clausius - Clapeyron equation. The markings are as shown in the diagram Slide 14,15 and 16 Demo Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Got IT Finally Instructions/ Working area Credits Step 1: Got It Finally Description of the Audio narration Text to be displayed action Show the above This is a graph to explain how the This is a graph to explain how the graph on the phase boundary relates the phase boundary relates the equilibrium screen and equilibrium temperature and temperature and pressure . As the markings without pressure . As the applied pressure on applied pressure on the substance is the dotted lines. the substance is varied the varied the equilibrium shifts to new When the last equilibrium shifts to new parameters parameters and leads to a change in line(marked In red) and leads to a change in equilibrium equilibrium temperature . As in the of the audio temperature . As in the above case above case pressure is changed from P narration starts, pressure is changed from P to (P+힓P) to (P+힓P) which shifts equilibrium then draw the which shifts equilibrium from E1 to from E1 to E2 where the temperature dotted lines and E2 where the temperature at E2 is at E2 is (T+힓T) the respective (T+힓T) markings Step 2: HOW DOES A PRESSURE COOKER WORK… Description of Audio narration Text to be displayed the action Show the Since boiling point is defined as the temperature at which Same as the audio above graph the external pressure equals vapour pressure, boiling point narration on the screen of water can be changed by changing the external pressure. When the valve is placed on the lid of pressure cooker , its mass determines the pressure inside the chamber because gas can escape through the pores only when it exceeds certain pressure. Hence the increased external pressure shifts the equilibrium point to some other position along the curve and thus the boiling point of water is increased. This reduces the consumption of heat energy and time as energy is not consumed for vapourising water at this temperature. Step 3: Ice skiing and espresso coffee machine Description of Audio narration Text to be displayed the action The negative slope of the co-existence curve for Same as the audio phase transition in case of ice and water is the narration reason for ice-skiing possible even in temperatures less than 0℃. When at constant temperature, ice is compressed resulting in its melting , this makes it self-lubricating and hence skiing is possible. Similar is the case with a ESPRESSO COFFEE MACHINE where on application of external pressure, water doesn’t boil even at 100 ℃ . Water at this temperature then enhances coffee taste with the beans and hence, espresso coffee tastes better than normal coffee. Master Layout 4 Phase transformation in Iron The above is the graph to be displayed. Show the markings and the scale of the graph as shown Slide 19 and 20 Demo Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Phase Transformation in Iron Instructions/ Working area Credits Step 1: Phase transformation in Iron Description Audio Text to be displayed of the action narration Show the Above is the graph Above is the graph which shows the effect of pressure on the which shows the above graph effect of pressure equilibrium temperature of phase transition for PURE IRON. The on the on the equilibrium solid – liquid phase transition in case of pure iron behaves normally temperature of and the equilibrium temperature increases gradually with phase transition for PURE IRON. The increasing pressure. solid – liquid phase Here, (dP/dT) =*∆ H/ T ∆V+ is positive since ∆V is positive from transition in case of solid to liquid transition . pure iron behaves normally and the But the effect of pressure is different for transition of one allotrope equilibrium of pure iron into other in the SOLID PHASE. There are 3 allotropes temperature of iron, namely α , γ , δ , iron in the normal pressure range while a increases gradually with increasing fourth allotrope ε-iron exists in high pressure range. pressure. Since we know, (dG/dP)=V at constant temperature, equilibrium temperature changes with change in temperature because these allotropes having different molar volumes , will have different changes in G. Step 2: Phase transformation in Iron Description Audio Text to be displayed of the action narration Show the For α- γ phase transition, increasing pressure decreases above graph the equilibrium temperature. on the (dP/dT)= ∆H/T ∆V, Being FCC structure, closely packed γ-iron has smaller molar volume than α-iron making ∆V negative while ∆H is positive. This leads to a negative sign in the clausius-clapeyron equation and hence equilibrium temperature decreases with increase in pressure. Since ε-iron is stable at very high pressures as can be seen from the graph, it has the highest density amongst all the allotropes. Slide 22 Demo Working Interactions Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Clausius Clapeyron Activity Area Instructions/ Working area Credits DESCRIPTION AUDIO NARRATION TEXT Make the 3 boxes on top of screen, 2 in green and Select a material from one in grey as tabs to be selected by the user.
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