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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.

Instructions/ Working area

Credits

Why ?

Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Demo

Slide 5 and 6

Description of the action Audio narration Text to be displayed

Show the above picture on the screen and then the audio narration. .

You must have observed that cooking the same food in an open vessel requires more time and heat than cooking it in a pressure cooker…..Have you ever wondered why?

Step 1: Why?


The following text appears on the screen and the text is highlighted corresponding to the audio narration

After going through this learning aid, you will be able to answer WHY ….. 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...

Same as the audio narration

Step 2: Lets Answer Why?

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.


Credits

Getting into the Equation


Slide 9, 10 and 11


Show the above picture on the screen and show the bubbles moving in the tube upwards.

Let us consider a generalised case of a weightless movable piston(weightless is considered so as to neglect gravity) on a closed 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 1: Getting into the Equation

Description of the action Audio narration

Text to be displayed

Show the same picture as on the previous slide

The substance will stay in following equilibrium 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

𝞓𝑉. 𝑑𝑃𝑃2

𝑃1

= 𝞓𝑆. 𝑑𝑇𝑇2

𝑇1

Hence 𝑑𝑃

𝑑𝑇 =

𝞓𝑆

𝞓𝑇

Also 𝞓S = 𝞓𝐻

𝑇

So 𝑑𝑃

𝑑𝑇 =

𝞓𝐻

𝞓𝑉.𝑇 [CLAUSIUS-CLAPEYRON EQN.]

(𝞓H is average of two phases)


Description of the action

Audio Text to be displayed

Show the same picture on the screen

For liquid-gas transition 𝞓V ≈ Vg

Vg = 𝑛𝑅𝑇

𝑃

So 𝑑𝑃

𝑑𝑇 =

𝞓𝐻

𝑛𝑅𝑇2

[n is the number of moles, R is the universal gas constant and Vg Is the volume of gas. ] Integrating both the sides

ln𝑃2

𝑃1 = 𝞓𝐻

𝑅 (

1

𝑇1 −

1

𝑇2 )

Here 𝞓𝐻 is Latent Heat Of vapourization of 1 mole Now simialr case is with melting Just 𝞓𝐻 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


Credits

Got IT Finally


Slide 14,15 and 16


Audio narration Text to be displayed

Show the above graph on the screen and markings without the dotted lines. When the last line(marked In red) of the audio narration starts, then draw the dotted lines and the respective markings

This is a graph to explain how the phase boundary relates the equilibrium temperature and pressure . As the applied pressure on the substance is varied the equilibrium shifts to new parameters and leads to a change in equilibrium temperature . As in the above case pressure is changed from P to (P+𝞓P) which shifts equilibrium from E1 to E2 where the temperature at E2 is (T+𝞓T)

This is a graph to explain how the phase boundary relates the equilibrium temperature and pressure . As the applied pressure on the substance is varied the equilibrium shifts to new parameters and leads to a change in equilibrium temperature . As in the above case pressure is changed from P to (P+𝞓P) which shifts equilibrium from E1 to E2 where the temperature at E2 is (T+𝞓T)

Step 1: Got It Finally



Show the above graph on the screen

Since boiling point is defined as the temperature at which the external pressure equals vapour pressure, boiling point 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 2: HOW DOES A PRESSURE COOKER WORK…



The negative slope of the co-existence curve for phase transition in case of ice and water is the 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.


Step 3: Ice skiing and espresso coffee machine

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


Credits

Phase Transformation in Iron


Slide 19 and 20


Audio narration


Show the above graph on the

Above is the graph which shows the effect of pressure on the equilibrium temperature of phase transition for PURE IRON. The solid – liquid phase transition in case of pure iron behaves normally and the equilibrium temperature increases gradually with increasing pressure.

Above is the graph which shows the effect of pressure on the equilibrium temperature of phase transition for PURE IRON. The solid – liquid phase transition in case of pure iron behaves normally and the equilibrium temperature increases gradually with increasing pressure. Here, (dP/dT) =*∆ H/ T ∆V+ is positive since ∆V is positive from solid to liquid transition . But the effect of pressure is different for transition of one allotrope of pure iron into other in the SOLID PHASE. There are 3 allotropes of iron, namely α , γ , δ , iron in the normal pressure range while a fourth allotrope ε-iron exists in high pressure range. 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 1: Phase transformation in Iron


Audio narration


Show the above graph on the

For α- γ phase transition, increasing pressure decreases the equilibrium temperature. (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.

Step 2: Phase transformation in Iron


Credits

Clausius Clapeyron Activity Area

Working Interactions Tab 03 Tab 04 Tab 05 Tab 06 Tab 07 Demo

Slide 22

DESCRIPTION Make the 3 boxes on top of screen, 2 in green and one in grey as tabs to be selected by the user. Once they select 1 tab, accordingly the graph has to be selected from the 2 graphs given in another file. Then user will drag the piston up and down and as the piston moves ,the pressure will change on x axis by changing the level of the red colour and the corresponding equilibrium temperature rises on the y axis by changing the level of the colour .The scale will be chosen according to the given graph. you have to accordingly fill the entries of p vs t Graph and the pressure will increase on dragging down and decrease on dragging up . Also on dragging down the liquid in the figure shown increases but very gradually and molecules decreases and vice versa. Also for each reading two perpendicular dash lines will be made one to x and one to y which will cut axis on the level of red colour and write the values in a box near the intersection of these perpendicular lines indicating pressure and equilibrium temperature. If the person wishes to perform the same experiment for different material, then he can once again select the other tab.

AUDIO NARRATION Select a material from the given list to analise its pressure temperature relationship. now, move the piston either up or down to decrease or increase the pressure inside the vessel accordingly. This will enable you to view the equilibrium temperature inside the given box on variation of pressure. There is also a ‘graph’ tab on the screen which on clicking will directly display the graph of the selected material. If you wish to do the same for other material, then you can once again select a different material from the given list.

TEXT

Also, there will be one “graph” tab which on clicking will directly display the graph of the selected material . In that graph , also mark separately the “normal melting/boiling point” , which is the temperature at 1 atmosphere pressure and can be easily seen from the graph

Title – LETS TRY THIS OUT !

DESCRIPTION AUDIO NARRATION

TEXT TO BE DISPLAYED

The questionnaire series from. next slide begins with the title written above ,then appears this the question in red colour and next is this image. Now the heavy load attached, is pulled in the direction shown with a hand and the fine wire smoothly cuts the ice block. This cutting has to be shown with dark blue or white color. As the wire keeps on moving downwards, the ice block refreezes till the place where this wire just passed by.

Same as on next slide

Questionnaire LETS TRY THIS OUT !

1. Which phenomenon is shown in the animation below?

This is known as REGELATION.

When ice melts on application of high pressure and then it again refreezes when pressure is relieved, the concept is known as regelation.

An example is cutting a block of ice with a fine wire which is wound around it and pulled with high pressure. This enables the wire to pass through the block of ice and as soon as the wire passes through, block of ice refreezes.

2. Calculate the change in enthalpy (∆ H) for Methyl Chloride given that it’s transition temperature from liquid to gaseous phase at 1 atm. Pressure is -25⁰C and at 5 atm. Pressure is 23 ⁰C.

ANS– 20463.81 J

3. For the given conditions, calculate the transition temperature of fluorobenzene from liquid to gaseous phase at 0.8 atm if at .1 atm. pressure ,the temperature is 25⁰C and (∆ H) for this is 35255.61 J.

ANS– 76 ⁰C.

SUMMARY • CLAUSIUS – CLAPEYRON equation can be used to explain

the relationship between equilibrium transition temperature and pressure during the phase transition of any substance.

• There are different graphs for different elements having unique properties . Iron has a unique property of its existence in 4 allotropic forms in different physical conditions, helium has a graph which has a negative slope and then becomes positive after a minima. Unlike most materials , water has a negative slope in solid- liquid phase transition and so on.

• After going through this learning aid, we are able to answer why pressure cooker cooks faster, espresso coffee tastes better, ice skiing is possible in temperatures less than 0 degree celsius and many such queries.


Credits

Summary

Working Interactions Summary Tab 04 Tab 05 Tab 06 Tab 07 Demo

Slide 28

References

• Phase transformations in metals and alloys, D. A. Porter and K. E. Easterling, 2nd edition, Chapman And Hall.

clausius clapeyron equation - oscar …oscar.iitb.ac.in/oscarpp/metallurgical engineering...clausius...

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