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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 (K_B) and Temperature (T).

The formula for calculating shear modulus of rubber:

G = NK_BT

Where:

G = Shear Modulus of Rubber
N = Density of Network Cross Links
K_B = 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
K_B = Boltzmann’s Constant = 1.38064852E-23
T = Temperature = 10

G = NK_BT
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 / _K_BT

Where;

N = Density of Network Cross Links
G = Shear Modulus of Rubber
K_B = 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
K_B = Boltzmann’s Constant = 1.380e-23
T = Temperature = 4

N = ^G / _K_BT
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 (Q_s), Boltzmann’s Constant (K) and Temperature (T).

The formula for calculating schottky defect:

N_s = N exp (^-Q_s/_2KT)

Where:

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

N_s = N exp (^-Q_s/_2KT)
N_s = (22)exp(^-(44)/_{2(1.38064852e-23)(30)})
N_s = (22)exp(^(-44)/_{(8.283891119e-22)})
N_s = (22)exp(-5.3115135583771414e+22)
N_s = (22)(0)
N_s = 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 = ^N_s / _{e (^-Q_s /}_2KT)

Where;

N_s = Schottky Defect
Q_s = 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;

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

N = ^N_s / _{e (^-Q_s /}_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 N 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 (Q_fr), Boltzmann’s Constant (K) and temperature (T).

The formula for calculating the frenkel defect:

N_fr = N exp (^-Q_fr/ _2KT)

Where:

N_fr = Frenkel Defect
Q_fr = 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;

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

N_fr = N exp (^-Q_fr/ _2KT)
N_fr = (22)exp(^-(34)/ _{2(1.38064852e-23)(14)})
N_fr = (22)exp(^(-34)/ _{(3.865815856e-22)})
N_fr = (22)exp(-8.795038684325786e+22)
N_fr = (22)(0)
N_fr = 0

Therefore, the frenkel defect is 0.

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

Q_fr = – (In (^N_fr / _N) x 2KT)

Where;

Q_fr = Activation Energy
N_fr = 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;

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

Q_fr = – (In (^N_fr / _N) x 2KT)
Q_fr = – (In (²⁰ / ₁₀) x 2 x 5 x 2)
Q_fr = – (In 2 x 20)
Q_fr = – (In 40)
Q_fr = – 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 (P_b^*) and Gas Gravity at Actual Separator P_sep and T_sep (γ_g).

The formula for calculating the glass gas solubility:

γ_gs = γ_g[(^(°API)0.989/ _{(T – 460)^0.172})P_b^*]^1.2255

Where:

γ_gs = Glass Gas Solubility
°API = API Gravity
T = Temperature (°Rankine)
P_b^* = Mean Bubble Point
γ_g = Gas Gravity at Actual Separator P_sep and T_sep

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
P_b^* = Mean Bubble Point = 40
γ_g = Gas Gravity at Actual Separator P_sep and T_sep = 54

γ_gs = γ_g[(^(°API)0.989 / _{(T – 460)^0.172})P_b^*]^1.2255
γ_gs = 54[(^(15)0.989 / _{(30 – 460)^0.172})40]^1.2255
γ_gs = 54[(^(15)0.989 / _(-430)0.172)40]^1.2255
γ_gs = 54[(^(15)0.989 / _(NaN))40]^1.2255
γ_gs = 54[(^14.5 / _NaN)40]^1.2255
γ_gs = 54[(NaN)40]^1.2255
γ_gs = 54[NaN]^1.2255
γ_gs = 54[NaN]
γ_gs = 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

How to Calculate and Solve for Separator Gas Gravity in a Fluid | The Calculator Encyclopedia

The image above represents separator gas gravity.

To compute for the separator gas gravity, four essential parameters are needed and these parameters are API Gravity (°API), Actual Separator Temperature (°Rankine) (T_sep), Actual Separator Pressure (P_sep) and Gas Gravity at Actual Separator P_sep and T_sep(γ_g).

The formula for calculating the separator gas gravity:

γ_gs = γ_g[1 + 5.912(10^-5)(°API)(T_sep – 460)log(^P_sep / _114.7)]

Where:

γ_gs = Separator Gas Gravity
°API = API Gravity
T_sep = Actual Separator Temperature (°Rankine)
P_sep = Actual Separator Pressure
γ_g = Gas Gravity at Actual Separator P_sep and T_sep

Let’s solve an example;
Find the separator gas gravity with an API Gravity of 21, actual separator temperature of 18, actual separator pressure of 14 and gas gravity at actual separator of 32.

This implies that;

°API = API Gravity = 21
T_sep = Actual Separator Temperature (°Rankine) = 18
P_sep = Actual Separator Pressure = 14
γ_g = Gas Gravity at Actual Separator P_sep and T_sep = 32

γ_gs = γ_g[1 + 5.912(10^-5)(°API)(T_sep – 460)log(^P_sep / _114.7)]
γ_gs = 32[1 + 5.912(10^-5)(21)(18 – 460)log(¹⁴ / _114.7)]
γ_gs = 32 [1 + 5.912(10^-5)(21)(18 – 460) log(0.1220)]
γ_gs = 32 [1 + 5.912(10^-5)(21)(-442) log(0.1220)]
γ_gs = 32 [1 + 5.912(10^-5)(21) (-442) (-0.9134)]
γ_gs = 32 [1 + 0.501]
γ_gs = 32 [1.501]
γ_gs = 48.039

Therefore, the separator gas gravity is 48.039.

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

How to Calculate and Solve for Gas Formation Volume Factor (FVF) | The Calculator Encyclopedia

The image above represents the gas FVF.

To compute for the gas FVF, three essential parameters are needed and these parameters are Z-Factor (Z), Temperature (T) and Pressure (P).

The formula for calculating the gas FVF:

B_g = 0.00504[^ZT / _P]

Where;

B_g = Gas FVF
Z = Z-Factor
T = (°R) Temperature
P = Pressure

Let’s solve an example;
Find the Gas FVF when the Z-Factor is 12, temperature is 30 and the pressure is 120.

This implies that;

Z = Z-Factor = 12
T = (°R) Temperature = 30
P = Pressure = 120

B_g = 0.00504[^ZT / _P]
B_g = 0.00504[^{12 x 30} / ₁₂₀]
B_g = 0.00504[³⁶⁰ / ₁₂₀]
B_g = 0.00504[3]
B_g = 0.01512

Therefore, the gas FVF is 0.01512 ^bbl / _scf.

Calculating for the Z-Factor when the Gas FVF, Temperature and Pressure is Given.

Z = ^B_g.P / _0.00504T

Where;

Z = Z-Factor
B_g = Gas FVF
T = (°R) Temperature
P = Pressure

Let’s solve an example;
Find the Z-Factor when the Gas FVF is 22, temperature is 16 and the pressure is 80.

This implies that;

B_g = Gas FVF = 22
T = (°R) Temperature = 16
P = Pressure = 80

Z = ^B_g.P / _0.00504T
Z = ^{22 x 80} / _{0.00504 x 16}
Z = ¹⁷⁶⁰ / _0.08064
Z = 21825.39

Therefore, the Z-Factor is 21825.39.

Calculating for the Temperature when the Gas FVF, Z-Factor and the Pressure is Given.

T = ^B_g.P / _0.00504Z

Where;

T = (°R) Temperature
Z = Z-Factor
B_g = Gas FVF
P = Pressure

Let’s solve an example;
Find the Temperature when the Gas FVF is 44, Z-Factor is 29 and the pressure is 70.

This implies that;

Z = Z-Factor = 29
B_g = Gas FVF = 44
P = Pressure = 70

T = ^B_g.P / _0.00504Z
T = ^{44 x 70} / _{0.00504 x 29}
T = ³⁰⁸⁰ / _0.14616
T = 21072.79

Therefore, the temperature is 21072.79.

Continue reading How to Calculate and Solve for Gas Formation Volume Factor (FVF) | The Calculator Encyclopedia

How to Calculate and Solve for Temperature, Number of Moles, Volume, Van’t Hoff Factor and Osmotic Pressure | The Calculator Encyclopedia

The image above represents the osmotic pressure.

To compute for the osmotic pressure, five parameters are needed and these parameters are Ideal Gas Constant (R), Temperature in Kelvin (T), Number of Moles (n), Volume (V) and Van’t Hoff’s Factor (i).

The formula for calculating osmotic pressure:

π = i ^nRT ⁄ _V

Where;
π = osmotic pressure
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
i = Van’t Hoff’s Factor
V = Volume

Let’s solve an example;
Find the osmotic pressure when the ideal gas constant is 0.08206 with a temperature in kelvin of 120, number of moles is 32, a volume of 48 and a van’t hoff’s factor of 24.

This implies that;
n = number of moles = 32
R = ideal gas constant = 0.08206
T = temperature in Kelvin = 120
i = Van’t Hoff’s Factor = 24
V = Volume = 48

π = i ^nRT ⁄ _V
π = 24 ^{32 x 0.08206 x 120} ⁄ ₄₈
π = (24) ^(315.110) ⁄ ₍₄₈₎
π = (24)(6.5647)
π = 157.5

Therefore, the osmotic pressure is 157.5 atm.

Calculating the Van’t Hoff’s Factor using the Osmotic Pressure, Number of Moles, Temperature in Kelvin, Ideal Gas Constant and Volume.

i = ^Vπ / _nRT

Where;
i = Van’t Hoff’s Factor
π = osmotic pressure
V = Volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin

Let’s solve an example;
Find the Van’t Hoff’s Factor when the osmotic pressure is 220, volume of 50, temperature in kelvin of 180 and number of moles of 60. (R = 0.08206)

This implies that;
π = osmotic pressure = 220
V = Volume = 50
n = number of moles = 60
R = ideal gas constant = 0.08206
T = temperature in Kelvin = 180

i = ^Vπ / _nRT
i = ^{50 x 220} / _{60 x 0.08206 x 180}
i = ¹¹⁰⁰⁰ / _866.808
i = 12.69

Therefore, the Van’t Hoff’s Factor is 12.69.

Calculating the Volume using the Osmotic Pressure, Number of Moles, Temperature in Kelvin, Ideal Gas Constant and Van’t Hoff’s Factor.

V = ^{i (nRT)} / _π

Where;
V = Volume
i = Van’t Hoff’s Factor
π = osmotic pressure
n = number of moles
R = ideal gas constant
T = temperature in Kelvin

Let’s solve an example;
Find the volume when the osmotic pressure is 280, Van’t Hoff’s Factor of 40, temperature in kelvin of 90 and number of moles of 70. (R = 0.08206)

This implies that;
i = Van’t Hoff’s Factor = 40
π = osmotic pressure = 280
n = number of moles = 70
R = ideal gas constant = 0.08206
T = temperature in Kelvin = 90

V = ^{i (nRT)} / _π
V = ^{40 (70 x 0.08206 x 90)} / ₂₈₀
V = ^{40 (516.978)} / ₂₈₀
V = ^20679.12 / ₂₈₀
V = 73.854