How to Calculate and Solve for Permeability | Mass Transfer

The image above represents permeability.

To compute for permeability, five essential parameters are needed and these parameters are Constant (A), Partial Pressure (Po), Activation due to Permeation (Qp), Gas Constant (R) and Temperature (T).

The formula for calculating permeability:

P = APo0.5 . e-Qp/RT

Where:

P = Permeability
A = Constant
Po = Partial Pressure
Qp = Activation due to Permeation
R = Gas Constant
T = Temperature

Let’s solve an example;
Find the permeability when the constant is 12, the partial pressure is 22, the activation due to permeation is 10, the gas constant is 14 and the temperature is 2.

This implies that;

A = Constant = 12
Po = Partial Pressure = 22
Qp = Activation due to Permeation = 10
R = Gas Constant = 14
T = Temperature = 2

P = APo0.5 . e-Qp/RT
P = 12(22)0.5 . e-(10)/(14)(2)
P = 12(4.69) . e-10/28
P = 56.28 . e-0.357
P = 56.28 (0.699)
P = 39.38

Therefore, the permeability is 39.38.

Continue reading How to Calculate and Solve for Permeability | Mass Transfer

How to Calculate and Solve for Knudsen Diffusion of Moulding Sand | Mass Transfer

The image above represents knudsen diffusion of moulding sand.

To compute for knudsen diffusion of moulding sand, three essential parameters are needed and these parameters are Pore Radius (r), Temperature (T) and Molecular Weight (M).

The formula for calculating knudsen diffusion of moulding sand:

Dk = 9700r√(T/M)

Where:

Dk = Knudsen Diffusion of Moulding Sand
r = Pore Radius
T = Temperature
M = Molecular Weight

Let’s solve an example;
Find the knudsen diffusion of moulding sand when the pore radius is 24, the temperature is 18 and the molecular weight is 12.

This implies that;

r = Pore Radius = 24
T = Temperature = 18
M = Molecular Weight = 12

Dk = 9700r√(T/M)
Dk = 9700(24)√(18/12)
Dk = 9700(24)√(1.5)
Dk = 9700(24)(1.22)
Dk = 285120.6

Therefore, the knudsen diffusion of moulding sand is 285120.6 cm²/s.

Calculating the Pore Radius when the Knudsen Diffusion of Moulding Sand, the Temperature and the Molecular Weight is Given.

r = Dk / 9700 √(T / M)

Where:

r = Pore Radius
Dk = Knudsen Diffusion of Moulding Sand
T = Temperature
M = Molecular Weight

Let’s solve an example;
Find the pore radius when the knudsen diffusion of moulding sand is 20, the temperature is 14 and the molecular weight is 10.

This implies that;

Dk = Knudsen Diffusion of Moulding Sand = 20
T = Temperature = 14
M = Molecular Weight = 10

r = Dk / 9700 √(T / M)
r = 20 / 9700 √(14 / 10)
r = 20 / 9700 √(1.4)
r = 20 / 11446
r = 0.00174

Therefore, the pore radius is 0.00174.

Continue reading How to Calculate and Solve for Knudsen Diffusion of Moulding Sand | Mass Transfer

How to Calculate and Solve for Stokes-Einstein Equation of Diffusivity | Mass Transfer

The image above represents strokes-einstein equation of diffusivity.

To compute for strokes-einstein equation of diffusivity, four essential parameters are needed and these parameters are Boltzmann’s Constant (KB), Temperature (T), Radius of Sphere (R) and Viscosity (η).

The formula for calculating strokes-einstein equation of diffusivity:

D = KBT / 6πRη

Where:

D = Diffusivity
KB = Boltzmann’s Constant
T = Temperature
R = Radius of Sphere
η = Viscosity

Let’s solve an example;
Find the diffusivity when the boltzmann’s constant is 1.3806E-23, the temperature is 22, the radius of sphere is 12 and the viscosity is 10.

This implies that;

KB = Boltzmann’s Constant = 1.3806E-23
T = Temperature = 22
R = Radius of Sphere = 12
η = Viscosity = 10

D = KBT / 6πRη
D = (1.3806e-23)(22) / 6π(12)(10)
D = 3.037e-22 / 2261.94
D = 1.342

Therefore, the diffusivity is 1.342e-25 cm²/s.

Continue reading How to Calculate and Solve for Stokes-Einstein Equation of Diffusivity | Mass Transfer

How to Calculate and Solve for Relationship between Electrical Conductivity and Diffusivity | Mass Transfer

The image above represents relationship between electrical conductivity and diffusivity.

To compute for relationship between electrical conductivity and diffusivity, five essential parameters are needed and these parameters are Electrical conductivity (σ ), Coordination Number (Z), Electron Charge (e), Boltzmann’s Constant (KB) and Temperature (T).

The formula for calculating relationship between electrical conductivity and diffusivity:

σ/D = n(Ze)² / KBT

Where:

σ/D = Relationship between Electrical Conductivity and Diffusivity
σ = Electrical Conductivity
D = Diffusivity
Z = Coordination Number
e = Electron Charge
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the relationship between electrical conductivity and diffusivity when the electrical conductivity is 2, the coordination number is 3, the electron charge is 4, the boltzmann’s constant is 1.3806e-23 and the temperature is 7.

This implies that;

σ = Electrical Conductivity = 2
Z = Coordination Number = 3
e = Electron Charge = 4
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 7

σ/D = n(Ze)² / KBT
σ/D = 2(3(4))² / 1.3806e-23(7)
σ/D = 2(12)² / 9.66e-23
σ/D = 2(144) / 9.66e-23
σ/D = 288 / 9.66e-23
σ/D = 2.97

Therefore, the relationship between electrical conductivity and diffusivity is 2.97e+24.

Continue reading How to Calculate and Solve for Relationship between Electrical Conductivity and Diffusivity | Mass Transfer

How to Calculate and Solve for Diffusion Coefficient | Mass Transfer

The image above represents diffusion coefficient.

To compute for diffusion coefficient, three essential parameters are needed and these parameters are Constant (BA), Boltzmann’s Constant (KB) and Temperature (T).

The formula for calculating diffusion coefficient:

DA = BAKBT

Where:

DA = Diffusion Coefficient | Nernst-Einstein Equation
BA = Constant
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the diffusion coefficient when the constant is 21, the boltzmann’ s constant is 1.39e-23 and temperature is 12.

This implies that;

BA = Constant = 21
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 12

DA = BAKBT
DA = (21)(1.38e-23)(12)
DA = 3.47

Therefore, the diffusion coefficient is 3.47e-21 cm²/s.

Calculating the Constant when the Diffusion Coefficient and the Temperature is Given.

BA = DA / KB x T

Where;

BA = Constant
DA = Diffusion Coefficient | Nernst-Einstein Equation
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the constant when the diffusion coefficient is 10 and the temperature is 3.

This implies that;

DA = Diffusion Coefficient | Nernst-Einstein Equation = 10
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 12

BA = DA / KB x T
BA = 10 / 1.3806e-23 x 12
BA = 10 / 1.70e-9
BA = 5.88e+9

Therefore, the constant is 5.88e+9.

Continue reading How to Calculate and Solve for Diffusion Coefficient | Mass Transfer

How to Calculate and Solve for Shear Modulus of Rubber | Fracture Mechanics

The image above represents shear modulus of rubber.

To compute for shear modulus of rubber, three essential parameters are needed and these parameters are Density of Network Cross Links (N), Boltzmann’s Constant (KBand Temperature (T).

The formula for calculating shear modulus of rubber:

G = NKBT

Where:

G = Shear Modulus of Rubber
N = Density of Network Cross Links
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the shear modulus of rubber when the density of network cross links is 21, the boltzmann’s constant is 1.38064852E-23 and the temperature is 10.

This implies that;

N = Density of Network Cross Links = 21
KB = Boltzmann’s Constant = 1.38064852E-23
T = Temperature = 10

G = NKBT
G = (21)(1.38064852e-23)(10)
G = 2.89

Therefore, the shear modulus of rubber is 2.89e-23 Pa.

Calculating the Density of Network Cross Links when the Shear Modulus of Rubber, Boltzmann’s Constant and the Temperature is Given.

N = G / KBT

Where;

N = Density of Network Cross Links
G = Shear Modulus of Rubber
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the density of network cross links when the shear modulus of rubber is 14, the boltzmann’s constant is 1.380e-23 and temperature is 4.

This implies that;

G = Shear Modulus of Rubber = 14
KB = Boltzmann’s Constant = 1.380e-23
T = Temperature = 4

N = G / KBT
N = 14 / 1.380e-23 x 4
N = 14 / 5.52e-23
N = 2.54e-23

Therefore, the network cross links is 2.54e-23.

Continue reading How to Calculate and Solve for Shear Modulus of Rubber | Fracture Mechanics

How to Calculate and Solve for Schottky Defect | Ceramics

The image above represents schottky defect.

To compute for schottky defect, four essential parameters are needed and these parameters are N, Activation energy (Qs), Boltzmann’s Constant (K) and Temperature (T).

The formula for calculating schottky defect:

Ns = N exp (-Qs/2KT)

Where:

Qs = Activation Energy
K = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the schottky defect when the activation energy is 44, N is 22, boltzmann’s constant is 1.38064852E-23 and the temperature is 30.

This implies that;

N = 22
Qs = Activation Energy = 44
K = Boltzmann’s Constant = 1.38054852E-23
T = Temperature = 30

Ns = N exp (-Qs/2KT)
Ns = (22)exp(-(44)/2(1.38064852e-23)(30))
Ns = (22)exp((-44)/(8.283891119e-22))
Ns = (22)exp(-5.3115135583771414e+22)
Ns = (22)(0)
Ns = 0

Therefore, the schottky defect is 0.

Calculating the N when the Schottky Defect, the Activation Energy, the Boltzmann’s Constant and the Temperature is Given.

N = Ns / e (-Qs / 2KT)

Where;

Ns = Schottky Defect
Qs = Activation Energy
K = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the N when the schottky defect is 40, the activation energy is 24, the boltzmann’s constant is 1.38064852E-23 and the temperature is 10.

This implies that;

Ns = Schottky Defect = 40
Qs = Activation Energy = 24
K = Boltzmann’s Constant = 1.38064852E-23
T = Temperature = 10

N = Ns / e (-Qs / 2KT)
N = 40 / e (-24 / 2 x 1.38064852E-23 x 10)
N = 40 / e (-24 / 2.76129704E+23)
N = 40 / e (8.691567e-23)
N = 40 / 8.691567e+23
N = 4.602e-23

Therefore, the is 4.602e-23.

Continue reading How to Calculate and Solve for Schottky Defect | Ceramics

How to Calculate and Solve for Frenkel Defect | Ceramics

The image above represents frenkel defect.

To compute for frenkel defect, four essential parameters are needed and these parameters are N, activation energy (Qfr), Boltzmann’s Constant (K) and temperature (T).

The formula for calculating the frenkel defect:

Nfr = N exp (-Qfr / 2KT)

Where:

Nfr = Frenkel Defect
Qfr = Activation Energy
K = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the frenkel defect when the activation energy is 34, N is 22, Temperature is 12 and the boltzmann’s constant is 1.38064852e-23.

This implies that;

Qfr = Activation Energy
K = Boltzmann’s Constant
T = Temperature

Nfr = N exp (-Qfr / 2KT)
Nfr = (22)exp(-(34) / 2(1.38064852e-23)(14))
Nfr = (22)exp((-34) / (3.865815856e-22))
Nfr = (22)exp(-8.795038684325786e+22)
Nfr = (22)(0)
Nfr = 0

Therefore, the frenkel defect is 0.

Calculating the Activation Energy when the Frenkel Defect, the Boltzmann’s Constant and the Temperature is Given.

Qfr = – (In (Nfr / N) x 2KT)

Where;

Qfr = Activation Energy
Nfr = Frenkel Defect
K = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Given that the frenkel defect is 20, the boltzmann’s constant is 5, the temperature is 2 and N is 10. Find the activation energy?

This implies that;

Nfr = Frenkel Defect = 20
K = Boltzmann’s Constant = 5
T = Temperature = 2
N = 10

Qfr = – (In (Nfr / N) x 2KT)
Qfr = – (In (20 / 10) x 2 x 5 x 2)
Qfr = – (In 2 x 20)
Qfr = – (In 40)
Qfr = – 3.688

Therefore, the activation energy is – 3.688.

Continue reading How to Calculate and Solve for Frenkel Defect | Ceramics

How to Calculate and Solve for Standing Bubble Point Parameter | The Calculator Encyclopedia

The image above represents standing bubble point parameter.

To compute for the standing bubble point parameter, two essential parameters are needed and these parameters are API Gravity (°API) and Temperature (°Rankine) (T).

The formula for calculating standing bubble point parameter:

a = [0.00091(T – 460)] – [0.0125(°API)]

Where:

a = Standing Bubble Point Parameter, a
°API = API Gravity
T = Temperature (°Rankine)

Let’s solve an example;
Find the standing bubble point parameter when API Gravity is 32 and the temperature is 146.

This implies that:

°API = API Gravity = 32
T = Temperature (°Rankine) = 146

a = [0.00091(T – 460)] – [0.0125(°API)]
a = [0.00091(146 – 460)] – [0.0125(32)]
a = [0.00091(-314)] – [0.0125(32)]
a = [-0.28574] – [0.0125(32)]
a = [-0.28574] – [0.4]
a = -0.68574

Therefore, the standing bubble point parameter, a is -0.68574.

Continue reading How to Calculate and Solve for Standing Bubble Point Parameter | The Calculator Encyclopedia

How to Calculate and Solve for Glass Gas Solubility in a Fluid | The Calculator Encyclopedia

The image above represents glass gas solubility.

To compute for the glass gas solubility, four essential parameters are needed and these parameters are API Gravity (°API), Temperature (°Rankine) (T), Mean Bubble Point (Pb*) and Gas Gravity at Actual Separator Psep and Tsepg).

The formula for calculating the glass gas solubility:

γgs = γg[((°API)0.989 / (T – 460)0.172)Pb*]1.2255

Where:

γgs = Glass Gas Solubility
°API = API Gravity
T = Temperature (°Rankine)
Pb* = Mean Bubble Point
γg = Gas Gravity at Actual Separator Psep and Tsep

Let’s solve an example;
Find the glass gas solubility when the API Gravity is 15, the temperature is 30, the mean bubble point is 40 and the gas gravity at actual separator is 54.

This implies that;

°API = API Gravity = 15
T = Temperature (°Rankine) = 30
Pb* = Mean Bubble Point = 40
γg = Gas Gravity at Actual Separator Psep and Tsep = 54

γgs = γg[((°API)0.989 / (T – 460)0.172)Pb*]1.2255
γgs = 54[((15)0.989 / (30 – 460)0.172)40]1.2255
γgs = 54[((15)0.989 / (-430)0.172)40]1.2255
γgs = 54[((15)0.989 / (NaN))40]1.2255
γgs = 54[(14.5 / NaN)40]1.2255
γgs = 54[(NaN)40]1.2255
γgs = 54[NaN]1.2255
γgs = 54[NaN]
γgs = NaN

Therefore, the glass gas solubility is NaN.

Continue reading How to Calculate and Solve for Glass Gas Solubility in a Fluid | The Calculator Encyclopedia