Kinetic Theory (5, 8)

These equations describe properties of an ideal gas.

Equations:

P =

n ⋅ MW ⋅ vrms2

 

 

 

--------------------------------------3 ⋅ V

 

 

 

 

 

 

 

 

λ =

 

1

 

 

 

 

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

n ⋅ NA

 

 

 

2 ⋅ π ⋅

⋅ d

2

 

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

V

 

 

 

 

 

 

 

vrms =

3------------------- R ⋅ T

 

MW

m = n ⋅ MW

Example:

Given: P=100_kPa, V=2_1, T=26.85_°C, MW=18_g/gmol, d=2.5_nm.

Solution: vrms=644.7678_m/s, m=1.4433E–3_kg, n=0.0802_gmol, λ=1.4916_nm.

Heat Transfer (6)

Variable Description

αExpansion coefficient

δElongation

λ1, λ2

Lower and upper wavelength limits

λmax

Wavelength of maximum emissive power

ΔT

Temperature difference

AArea

cSpecific heat

eb12

Emissive power in the range λ1 to λ2

eb

Total emissive power

fFraction of emissive power in the range λ1 to λ2

h, h1,h3 Convective heat-transfer coefficient

k, k1, k2, k3

Thermal conductivity

L, L1, L2, L3

Length

mMass

QHeat capacity

qHeat transfer rate

TTemperature

Tc

Cold surface temperature (Conduction), or

Cold fluid temperature

 

Th

Hot surface temperature, or

Hot fluid temperature (Conduction + Convection)

 

Ti, Tf

Initial and final temperature

UOverall heat transfer coefficient

References: 7, 9.

5-28 Equation Reference