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The First Law

PVT relationships

The Second Law

Energy for process

Prediction of equilibrium state and properties and engineering analysis of system

(physical, chemical, or biological)

Mathematical formalism and generalization

Path forward from two great laws of nature

Laws

Property data, models correlations

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Fundamental property relations

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Exact Differential equation

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Maxwell relations

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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H(T, P)

 

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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S(T, P)

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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U(P) at dT=0

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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U(T, V) and S (T,V)

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Question

Estimate the change in enthalpy and entropy when liquid ammonia at 270 K is compressed from its saturation pressure of 381 kPa to 1200 kPa.

​

For saturated liquid ammonia at 270 K,

Vl = 1.551 × 10-3 m3·kg-1, and β = 2.095 × 10-3 K-1.

�

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Gibbs Energy as a Generating Function

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Helmholtz Energy as a Generating Function

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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The Gibbs energy, G or G/RT ,

when given as a function of its canonical variables T & P,

serves as a generating function for the other thermodynamic properties

through simple mathematics

and implicitly represents complete property information

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​

( Also, A (T,V) or A/RT(T, V))

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Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Fundamental Residual Property

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Fundamental Residual Property

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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P bar

T = 340 K

350 K

360 K

370 K

380 K

0.10

0.99700

0.99719

0.99737

0.99753

0.99767

0.50

0.98745

0.98830

0.98907

0.98977

0.99040

2.00

0.95895

0.96206

0.96483

0.96730

0.96953

4.00

0.92422

0.93069

0.93635

0.94132

0.94574

6.00

0.88742

0.89816

0.90734

0.91529

0.92223

8.00

0.84575

0.86218

0.87586

0.88745

0.89743

10.0

0.79659

0.82117

0.84077

0.85695

0.87061

12.0

……

0.77310

0.80103

0.82315

0.84134

14.0

……

……

0.75506

0.78531

0.80923

15.41

……

……

0.71727

​

​

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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P bar

T = 340 K

350 K

360 K

370 K

380 K

0.10

0.99700

0.99719

0.99737

0.99753

0.99767

0.50

0.98745

0.98830

0.98907

0.98977

0.99040

2.00

0.95895

0.96206

0.96483

0.96730

0.96953

4.00

0.92422

0.93069

0.93635

0.94132

0.94574

6.00

0.88742

0.89816

0.90734

0.91529

0.92223

8.00

0.84575

0.86218

0.87586

0.88745

0.89743

10.0

0.79659

0.82117

0.84077

0.85695

0.87061

12.0

……

0.77310

0.80103

0.82315

0.84134

14.0

……

……

0.75506

0.78531

0.80923

15.41

……

……

0.71727

​

​

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual properties

  • Experiment
  • 2-term virial EoS
  • Volume explicit EoS
  • Cubic equation of state
  • Lee/Kesler
  • Other models�

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property from Virial EoS (Pressure)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property from Virial EoS (Volume)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property from Virial EoS (Volume)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property from Virial EoS (Volume)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Empirical/corresponding state correlations

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Corresponding States

All fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor, and all deviate from ideal-gas state behavior to about the same degree.

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Corresponding States and acentric factor

 

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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TQ 1.

Use the shortcut vapor pressure equation to calculate the vapor pressure of propane at -12℃

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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TQ 2.

Liquid butane is pumped to a vaporizer as a saturated liquid under a pressure of 18.8 bar. The butane leaves the exchanger as a wet vapor of 90 percent quality and at essentially the same pressure as it entered.

​

From the following information, estimate the heat load on the vaporizer per

gram of butane entering.

​

For butane, Tc = 425.2 K; Pc = 3.797 MPa; and ω= 0.193. Use the shortcut method to estimate the temperature of the vaporizer, and the Peng-Robinson equation to determine the enthalpy of vaporization.

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property Generalized Property Correlations for Gases

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property Generalized Property Correlations for Gases

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property Generalized Property Correlations for Gases

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property Generalized Property Correlations for Gases

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property Generalized 2nd-Virial-Coefficient Correlations

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual Property Generalized 2nd-Virial-Coefficient Correlations

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Cubic EoS, especially PR EoS

 

https://demonstrations.wolfram.com/ResidualFunctionsForTheSRKAndPREquationsOfState/#more

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Cubic EoS

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Cubic EoS…..

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Residual properties

  • Expt.
  • 2-term virial EoS
  • Volume explicit EoS
  • Lee/Kesler tables
  • Pitzer’s correlations
  • Cubic equation of state
  • Other models�

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Question

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Phase equilibrium

Butane at -15 ℃ (maintain isothermal using heat transfer)

P1

P2 (; P2> P1)

or

P2 (; P2=P1)

|Q|

|Q|

|Q|

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Clausius/Clapeyron equation

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Phase Transition

 

 

 

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Phase Transition

​

Remind G=H-TS and dG=VdP-SdT

​

 

 

 

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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​

Clausius/Clapeyron equation

Nain Singh and Kishan Singh Rawat

pbs.org, Survey of India, India post, Google Doodle

The Indian explorer and cartographer performed altitude survey using the simple thermometer and boiling water.

Further Readings:- Thomsen, V. (1997). The boiling point of water. The Physics Teacher, 35(2), 98-99.

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Empirical/corresponding state correlations

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Corresponding States

All fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor, and all deviate from ideal-gas state behavior to about the same degree.

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Corresponding States and acentric factor

 

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Rh

i

i

​

i

i

RLow

​

Rhigh

i or Rmeta

RLow

​

0

0

R

Z roots trends

R is real root and i is imaginary root

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Thermodynamic diagram

PH Diagram

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Thermodynamic diagram

PH Diagram(methane)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Thermodynamic diagram

PH Diagram(1,1,1,2-Tetrafluoroethane)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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T-S and H-S Diagram()

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Thermodynamic diagram

PH Diagram

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Thermodynamic diagram

PH Diagram(methane)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Thermodynamic diagram

PH Diagram(1,1,1,2-Tetrafluoroethane)

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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T-S and H-S Diagram()

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Mollier (HS) diagram for steam.

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Steam tables

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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