Download presentation

Presentation is loading. Please wait.

Published byMario Grand Modified over 4 years ago

1
Thermodynamics and Statistical Mechanics Equations of State

2
Thermo & Stat Mech - Spring 2006 Class 22 Thermodynamic quantities Internal energy (U): the energy of atoms or molecules that does not give macroscopic motion. Temperature (T): a measure of the internal energy of a system. Heat (Q): a way to change internal energy, besides work. (Energy in transit.)

3
Thermo & Stat Mech - Spring 2006 Class 23 Laws of Thermodynamics First law: đQ – đW = dU Q – W = U Energy is conserved

4
Thermo & Stat Mech - Spring 2006 Class 24 Work done by a gas

5
Thermo & Stat Mech - Spring 2006 Class 25 Work done by a gas

6
Thermo & Stat Mech - Spring 2006 Class 26 Work done by a gas

7
Thermo & Stat Mech - Spring 2006 Class 27 Configuration Work Product of intensive variable times corresponding extensive variable: đ W = xdY Gas, Liquid, Solid:PdV Magnetic Material: BdM Dielectric Material:EdP

8
Thermo & Stat Mech - Spring 2006 Class 28 Equation of State For an ideal gas: PV = nRT P = pressure (N/m²)(or Pa) V = volume (m³) n = number of moles T = temperature (K) R = gas constant (8.31 J/(K·mole))

9
Thermo & Stat Mech - Spring 2006 Class 29 Ideal gas law Ideal gas law:PV = nRT In terms of molar volume, v = V/n, this becomes: Pv = RT, or P = RT/v

10
Thermo & Stat Mech - Spring 2006 Class 210 Real Substance

11
Thermo & Stat Mech - Spring 2006 Class 211 Real Substance

12
Thermo & Stat Mech - Spring 2006 Class 212 van der Waals equation of state v cannot be decreased indefinitely, so replace v by v – b. Then, Next account for intermolecular attraction which will reduce pressure as molecules are forced closer together. This term is proportional to v -2

13
Thermo & Stat Mech - Spring 2006 Class 213 van der Waals equation of state This equation has a critical value of T which suggests a phase change. The next slide shows graphs for several values of T.

14
Thermo & Stat Mech - Spring 2006 Class 214 van der Waals equation of state

15
Thermo & Stat Mech - Spring 2006 Class 215 Critical Values

16
Thermo & Stat Mech - Spring 2006 Class 216 van der Waals equation of state This can be expressed in term of dimensionless coordinates, P ', v ', and T ' with the following Substitutions:

17
Thermo & Stat Mech - Spring 2006 Class 217 van der Waals equation of state This can also be written,

18
Thermo & Stat Mech - Spring 2006 Class 218 Thermal Expansion Expansivity or Coefficient of Volume Expansion,.

19
Thermo & Stat Mech - Spring 2006 Class 219 Thermal Expansion Usually, is positive. An exception is water in the temperature range between 0° C and 4° C. Range of is about: 10 -3 for gasses. 10 -5 for solids.

20
Thermo & Stat Mech - Spring 2006 Class 220 Linear Expansion Coefficient of Linear Expansion,.

21
Thermo & Stat Mech - Spring 2006 Class 221 Relationship Between and

22
Thermo & Stat Mech - Spring 2006 Class 222 Compressibility Volume also depends on pressure. Isothermal Compressibility:

23
Thermo & Stat Mech - Spring 2006 Class 223 Bulk Modulus

24
Thermo & Stat Mech - Spring 2006 Class 224 A Little Calculus

25
Thermo & Stat Mech - Spring 2006 Class 225 Cyclical Relation

26
Thermo & Stat Mech - Spring 2006 Class 226 Application Suppose you need:

27
Thermo & Stat Mech - Spring 2006 Class 227 Application

Similar presentations

OK

Real gases 1.4 Molecular interactions 1.5 The van de Waals equation 1.6 The principle of corresponding states Real gases do not obey the perfect gas law.

Real gases 1.4 Molecular interactions 1.5 The van de Waals equation 1.6 The principle of corresponding states Real gases do not obey the perfect gas law.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google