Equations:

T

= --------

 

2

 

 

 

P

------

2-

-----

T0

2 +

(

k – 1

) ⋅

M

P0

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

-----------

 

 

 

 

 

ρ

=

T k – 1

 

 

 

 

ρ----0--

T----0--

k

-----------

=--T---- k – 1

T0

 

 

 

 

 

 

 

 

 

 

 

 

k + 1

 

 

 

 

 

 

 

 

 

 

 

-----------------------

A

 

1

⋅

2

⋅

 

k – 1

⋅ M

2  2

⋅ (k – 1)

-----

=

M----

k-----+-----1-

1 +

-----2------



 

At

 

 

 

 

 

 

 

 

 

Example:

Given: k=2, M=.9, T0=26.85_°C, T=373.15_K, ρ0=100_kg/m^3, P0=100_kPa, A=1_cm^2.

Solution: P=464.1152_kPa, At=0.9928_cm^2, ρ=215.4333_kg/m^3.

Real Gas Law (5, 6)

These equations adapt the ideal gas law to emulate real-gas behavior. (See “ZFACTOR” in Chapter 3.)

Equations:

P ⋅ V = n ⋅ Z ⋅ R ⋅ T

m = n ⋅ MW

Example:

Given: Pc=48_atm, Tc=298_K, P=5_kPa, V=10_1, MW=64_g/gmol, T=75_°C.

Solution: n=0.0173_gmol, m=1.1057E–3_kg.

Real Gas State Change (5, 7)

This equation adapts the ideal gas state-change equation to emulate real-gas behavior. (See “ZFACTOR” in Chapter 3.)

Equation:

Pf ⋅ Vf

=

Pi ⋅ Vi

----------------Zf ⋅ Tf

---------------Zi ⋅ Ti

Example:

Given: Pc=48_atm, Pi=100_kPa, Pf=50_kPa, Ti=75_°C, Tc=298_K, Vi=10_1, Tf=250_°C. (Remember Zf and Zi are automatically calculated using these variables)

Solution: Vf=30.1703_l.

Equation Reference 5-27