1.Revision on Thermodynamics

2. First Law of Thermodynamics

Statement:

Energy can not be created or destroyed and the total energy of a system is always constant.

Mathematical formula for a closed system:

U = Q + W

Where;

U: change in internal energy

Q: heat transferred to the system.

W: work done by the system.

3. First Law of Thermodynamics

Sign convention:

If energy transferred to the system as q or w:

Q = +ve, W = +ve

If energy transferred from the system as q or w:

Q = -ve, W = -ve

4. First Law of Thermodynamics

Recall:

-System

The part of the universe that we will study. It is separated from its surroundings by boundaries.

System may be:

a. Open ; mass & heat can transfer

b. Closed ; no mass transfer

c. Isolated ; no mass or heat transfer

5. 6. First Law of Thermodynamics

Internal Energy

7. First Law of Thermodynamics

Work:

work arising from a change in volume.

work done by a gas as it expands and drive back the atmosphere.

dw = -P ext .dV

For reversible process: dw = - PdV

P = system pressure

8. First Law of Thermodynamics

Heat:

Q = m C T or Q = n C T

C = specific heat ( J/mol. K) , (J/gm. K)

C v= specific heat at constant volume

C p= specific heat at constant pressure

9. First Law of Thermodynamics

Molar heat capacity:

energy of one mole of a substance. (J/mol. K).

10. First Law of Thermodynamics

Enthalpy: H = U + PV

Heat content at constant pressure.

H =

H = n Cp T; if Cp is independent on T

11. Ideal gas processes ( rev process)

For different processes:

n C p T n C vT n Cv t Zero Adiabatic n C p T n C vT - P.V -nR T n Cp T= H Isobaric n C p T n C vT Zero n Cv T= U Isochoric Zero Zero -Q nRT ln(V f /V i )= nRT ln (P f /P i ) Isothermal H U W Q 12. First Law of Thermodynamics

PVT Relation: (for ideal gas)

Isothermal :PV = const.

Isobaric: V/T = Const

Isochoric: P/T = Const

Adiabatic: T 2 /T 1= (V 1 /V 2 ) -1

P 1 V 1 = P 2 V 2 ; C P/C V=

C P C V= R

13. Sheet (1)

A sample containing of 1.0 mole of argon expands isothermally at 0 C from 22.4 dm 3to 44.8 dm 3 .Calculate Q, W, U, and H if the gas expands:

reversibly

against a constant external pressure equal to the final pressure of the gas

freely

14. Sheet (1)

2. The constant pressure heat capacity of a sample of a prefect gas was found to vary with temperature according to the expression:

C P / (J/K) = 20.17 + 0.3665T

Calculate Q, W, U, and H when the temperature is raised from 25C to 200C:

(a) at constant pressure,

(b) at constant volume.

15. Sheet (1)

3. An ideal gas undergoes the following sequences of mechanically reversible processes in a closed system;

a) From an initial state 70C and 1 bar, it is compressed adiabatically to 150 C.

b) It is then cooled from 150 to 70C at constant pressure.

c) Finally, it is expanded isothermally to its original state.

Calculate W, Q, U, and H of each of the three processes and for the entire cycle. Take Cp = (5/2)R and Cv = (3/2) R

16. Second Law of Thermodynamics

Direction of energy :

A spontaneous process is a process in which the final state is more probable than the initial state.

Every system which is left to itself will, on average, change toward a system of maximum entropy.

17. Second Law of Thermodynamics

Entropy definition:

A measure of disorder of the system.

S is equal to the heat Q it absorbs, divided by T.

18. Second Law of Thermodynamics Zero Reversible adiabatic Cp ln (T 2 /T 1 ) - R ln( P 2 /P 1 ) Any Process Cv ln (T 2 /T 1 ) Isochoric Cp ln (T 2 /T 1 ) Isobaric nR ln (V 2 /V 1 )Isothermal S Process 19. Sheet 1

4.A 40 kg casting (Cp= 0.5 kJ/kg k ) at of 450 C is quenched in a 150 kg of oil (Cp= 2.5 kJ/kg k) at 25 C. if there are no heat losses,what is the change in entropy of the casting, the oil, and both considered together.

20. Third Law

Law of zero entropy

S (at any T) = S (at 298 K) +

21. Sheet 1

5. Calculate the absolute entropy for water at 400 K, knowing that Cp(liq)=75.29 J/mol K, and Cp(vap) =28.85+0.012 T+ (0.110 6 ) /T 2. Knowing that the standard entropy for water equal 69.91 J/mol K and heat of vaporization Hv =44.016 kJ/mol.

22. Thermodynamic equilibrium

S is a measure of equilibrium during reversible adiabatic process or isentropic process.

To define equilibrium in process other than isentropic process we use free energies.

23.

Gibbs free energy

G = H TS

H = total energy

TS = unavailable energy

dG = VdP SdT = fn ( P, T)

G = 0 at constant T and P

G = -ve(The process will be spontaneous)

24.

Isothermal Process:

dG = VdPG = RT ln(P 2 /P 1 )

Isobaric process:

dG= -SdTG= - SdT

Isochoric Process:

G = VdP - - SdT

25.

Helmholtzfree energy

A = U TS

U = Total energy

TS = unavailable energy

dA = -PdV SdT

A = 0 at constant V and T

G = H TS = U + PV- TS = A + PV

G =A + (PV)

26. Sheet 1

6. Calculate G, A, and S for each of the following processes:

a) Reversible melting of 36 gm of ice at 1 atm and 0C.

b) Reversible vaporization 39 gm of C 6 H 6at its normal boiling point of 80

27. Sheet 1

7. A sample consisting of 1 mole of argon is taken through the following cyclic process:

a) Isobaric expansion at 1 atm from 25 to 50 liters.

b) Isochoric cooling at 50 liters from 1 to 0.5 atm.

c) Isothermal compression to the initial state.

Calculate U, H,S G, A for each step and for the cycle. Argon may be considered ideal gas with C v =3/2R, C p =5/2R

28. Thank you