Prepare for your exams
Get points
Guidelines and tips

Sell on Docsity

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study

Go to the blog

Thermodynamics: Phases and their transition, Lecture notes of Thermodynamics

Indian Institute of Science Thermodynamics

Phase diagram, Triple point of water, First order phase transformation, Clausius-Clapeyron equation, Second order phase transformation

Typology: Lecture notes

2018/2019

Uploaded on 08/07/2019

vinodchawlafake 🇮🇳

(1)

12 documents

1 / 9

This page cannot be seen from the preview

Don't miss anything!

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,Tfor its description. In gas or vapor phase, for instance, we use

equation of state such as pV =RT or (p+a/V2)·(V−b) = RT etc. These

equations are valid over a restricted range of p,V,T.

We plot here water’s T−Vdiagram (isobars) and p−Vdiagram

(isotherms) over a wide range of p,T,Vfor different values of pand T

respectively. We get the following,

Partial preview of the text

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 = 100o^ C, water exists as a liquid that is about to vaporize

(saturated liquid).

I At T = 100o^ C, as more heat is transferred, the saturated water

starts vaporizing, saturated liquid-vapor mixture – boiling.

I T remains constant at 100o^ C 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

Phase diagram

The saturated vapor / liquid line in both the T − V and p − V diagrams

suggests the temperature at which liquid changes to vapor phase changes

with pressure. Similarly, the pressure at phase change depends on

temperature.

Saturation temperature Tsat : temperature at which pure substance

changes phase at a given pressure.

Saturation pressure psat : pressure at which pure substance changes

phase at a given temperature.

I Start with ice at p = 100 KPa and add heat to it. Water

temperature will rise until T = Tsat ≈ 0 o^ 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 ≈ 100 o^ 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.

First order phase transition : co-existing phases

1. Condition of co-existence of phases

μ 1 (T , p) = μ 2 (T , p)

2. First derivative of G is discontinuous across phase boundary.

3. Volume and entropy are discontinuous across phase boundary

V =

( ∂G

∂p

and S = −

( ∂G

∂T

4. CP of mixture of two phases during phase transition is infinite

CP = T

∂S

∂T

→ ∞, and so is β =

V

∂V

∂T

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

Clausius-Clapeyron equation

We apply Gibbs condition G 1 (T , p) = G 2 (T , p) to study properties of

boundary of first order transition across which there is a discontinuous

change of S and V. A first order phase change is accompanied by latent

heat L = T ∆S and volume change.

Consider points A(T , p) and B(T + dT , p + dp) on phase transition line

A : G 1 (T , p) = G 2 (T , p) and B : G 1 (T + dT , p + dp) = G 2 (T + dT , p + dp)

Thermodynamics: Phases and their transition, Lecture notes of Thermodynamics

Related documents

Partial preview of the text

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 = 100o^ C, water exists as a liquid that is about to vaporize

(saturated liquid).

I At T = 100o^ C, as more heat is transferred, the saturated water

starts vaporizing, saturated liquid-vapor mixture – boiling.

I T remains constant at 100o^ C 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.

Phase diagram

The saturated vapor / liquid line in both the T − V and p − V diagrams

suggests the temperature at which liquid changes to vapor phase changes

with pressure. Similarly, the pressure at phase change depends on

temperature.

Saturation temperature Tsat : temperature at which pure substance

changes phase at a given pressure.

Saturation pressure psat : pressure at which pure substance changes

phase at a given temperature.

I Start with ice at p = 100 KPa and add heat to it. Water

temperature will rise until T = Tsat ≈ 0 o^ 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 ≈ 100 o^ 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.

First order phase transition : co-existing phases

1. Condition of co-existence of phases

2. First derivative of G is discontinuous across phase boundary.

3. Volume and entropy are discontinuous across phase boundary

V =

( ∂G

( ∂G

∂T

4. CP of mixture of two phases during phase transition is infinite

CP = T

∂S

∂T

V

∂V

∂T

Since co-existing phases have different entropies, system must absorb or

release heat during phase transition – latent heat

Clausius-Clapeyron equation

We apply Gibbs condition G 1 (T , p) = G 2 (T , p) to study properties of

boundary of first order transition across which there is a discontinuous

change of S and V. A first order phase change is accompanied by latent

heat L = T ∆S and volume change.

Consider points A(T , p) and B(T + dT , p + dp) on phase transition line

Taylor expanding about A and using Gibbs condition,

∂G 1

∂T

∂G 1

∂G 2

∂T

∂G 2

∂G 2

∂T

]

[(