Engg Thermodynamics - Lecture - 13 - Unit - 4 - Ideal Gas and Real Gas & TD Relations

 Ideal Gas

Imaginary Substance

Obeys the law of PV=RT

At low Pressure and High Temperature – density of gas Decreases

Real Gas

At High Pressure – Gas start to Deviate from Ideal Gas

Measuring of Deviation – Compressibility Factor

PV=ZRT

Z=PV / RT

Z = Vactual / Videal

For Ideal Gas Z = 1

For Real Gas Z > 1

Important Laws (Ideal Gas)

Boyle's Law (constant temperature)

P = constant / V

Charles Law (constant pressure)

V = constant x T

Gay-Lussac’s Law (constant volume)

P = constant x T

THE ENTHALPY OF ANY SUBSTANCE

h=u+pv

for an ideal gas h=u+RT

h=f(T)

dh=du+RdT

since R is constant

∆h=∆u+R∆T

=Cv∆T+R∆T

= (Cv+R)∆T

Since h is a function of T only,

Cp=(∂h/∂T)p

Entropy change of an ideal gas: (Eqn – 1)

From the general property relations

Q = W+ U

Tds=du+pdv

And for an ideal gas, du=CvdT, dh=CpdT, and pv=RT,

the entropy change between any two states 1 and 2

may be computed as given below

ds=du/T+p/Tdv

=CvdT/T+Rdv/v

S2-s1=Cv ln T2/T1+R ln v2/v1

.

Entropy change of an ideal gas: (Eqn -2)

From the general property relations

Tds=dh-vdp

ds=dh/T-v/T.dp

=Cp.dT/T-R.dp/p

S2-s1=Cp ln T2/T1-R ln p2/p1

Entropy change of an ideal gas: (Eqn – 3)

From the general property relations Since

R=Cp-Cv

S2-S1=Cp ln T2/T1-Cp ln p2/p1+ Cv ln p2/p1

S2-S1=Cp ln v2/v1+Cv ln p2/p1

Any one of three equations and may be used for

computing the entropy change between any two

states of an ideal gas.

MAXWELL’S EQUATION

Maxwell Eqn Relate – The Entropy to P,V and T

Q = U + W

Tds = du + pdv

du = Tds – pdv

MAXWELL’S EQUATION

Maxwell Eqn Relate – The Entropy to P,V and T

h = u + pv

Take Diff on bothSides

dh = du + d(pv)

= du + vdp + pdv

dh = Tds – pdv + vdp + pdv

dh = Tds + vdp

MAXWELL’S EQUATION

Maxwell Eqn Relate – The Entropy to P,V and T

By Helmoltz Function

a = u – Ts

da = du – d(Ts)

= du – Tds – sdT

= Tds – pdv – Tds – sdT

da = – pdv – sdT

MAXWELL’S EQUATION

Maxwell Eqn Relate – The Entropy to P,V and T

By Gibbs Function,

G = h – Ts

dg = dh – d(Ts)

= dh - Tds – sdT

= Tds + vdp - Tds – sdT

dg = vdp – sdT

MAXWELL’S EQUATION

Maxwell Eqn Relate – The Entropy to P,V and T

1 - du = Tds – pdv

2 - dh = Tds + vdp

3 - da = – pdv – sdT

4 - dg = vdp – sdT