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Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Formula

GoPressure of Real Gas using Peng Robinson Equation Formula

GoActual Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters Formula

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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Check FAQs

p = (\frac{[R] \cdot (T r \cdot T c)}{(V m,r \cdot V m,c) - b PR}) - (\frac{a PR \cdot α}{({(V m,r \cdot V m,c)}^{2}) + (2 \cdot b PR \cdot (V m,r \cdot V m,c)) - ({b PR}^{2})})

p - Pressure?T_r - Reduced Temperature?T_c - Critical Temperature?V_m,r - Reduced Molar Volume?V_m,c - Critical Molar Volume?b_PR - Peng–Robinson Parameter b?a_PR - Peng–Robinson Parameter a?α - α-function?[R] - Universal gas constant?

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Example

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Here is how the Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters equation looks like with Values.

Here is how the Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters equation looks like with Units.

Here is how the Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters equation looks like.

418.0492 = (\frac{8.3145 \cdot (10 \cdot 647)}{(11.2 \cdot 11.5) - 0.12}) - (\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5)) - ({0.12}^{2})})

418.0492Pa = (\frac{8.3145 \cdot (10 \cdot 647K)}{(11.2 \cdot 11.5m³/mol) - 0.12}) - (\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5m³/mol)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5m³/mol)) - ({0.12}^{2})})

418.0492 = (\frac{8.3145 \cdot (10 \cdot 647)}{(11.2 \cdot 11.5) - 0.12}) - (\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5)) - ({0.12}^{2})})

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Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Solution

Follow our step by step solution on how to calculate Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

FIRST Step Consider the formula

p = (\frac{[R] \cdot (T r \cdot T c)}{(V m,r \cdot V m,c) - b PR}) - (\frac{a PR \cdot α}{({(V m,r \cdot V m,c)}^{2}) + (2 \cdot b PR \cdot (V m,r \cdot V m,c)) - ({b PR}^{2})})

Next Step Substitute values of Variables

∴

p = (\frac{[R] \cdot (10 \cdot 647K)}{(11.2 \cdot 11.5m³/mol) - 0.12}) - (\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5m³/mol)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5m³/mol)) - ({0.12}^{2})})

Next Step Substitute values of Constants

∴

p = (\frac{8.3145 \cdot (10 \cdot 647K)}{(11.2 \cdot 11.5m³/mol) - 0.12}) - (\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5m³/mol)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5m³/mol)) - ({0.12}^{2})})

Next Step Prepare to Evaluate

∴

p = (\frac{8.3145 \cdot (10 \cdot 647)}{(11.2 \cdot 11.5) - 0.12}) - (\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5)) - ({0.12}^{2})})

Next Step Evaluate

∴

p = 418.0492041575Pa

LAST Step Rounding Answer

∴

p = 418.0492Pa

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Formula Elements

Variables

Constants

Pressure

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

Symbol: p

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Pressure

Reduced Temperature

Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.

Symbol: T_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Reduced Temperature

Critical Temperature

Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.

Symbol: T_c

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Critical Temperature

Reduced Molar Volume

Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.

Symbol: V_m,r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Reduced Molar Volume

Critical Molar Volume

Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.

Symbol: V_m,c

Measurement: Molar Magnetic SusceptibilityUnit: m³/mol

Note: Value can be positive or negative.

Formulas to find Critical Molar Volume

Peng–Robinson Parameter b

Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

Symbol: b_PR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Peng–Robinson Parameter b

Peng–Robinson Parameter a

Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

Symbol: a_PR

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Peng–Robinson Parameter a

α-function

α-function is a function of temperature and the acentric factor.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find α-function

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other Formulas to find Pressure

Go Pressure of Real Gas using Peng Robinson Equation

p = (\frac{[R] \cdot T}{V m - b PR}) - (\frac{a PR \cdot α}{({V m}^{2}) + (2 \cdot b PR \cdot V m) - ({b PR}^{2})})

Go Actual Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters

p = P r \cdot (0.45724 \cdot ({[R]}^{2}) \cdot \frac{{(\frac{T}{T r})}^{2}}{a PR})

Other formulas in Peng Robinson Model of Real Gas category

Go Temperature of Real Gas using Peng Robinson Equation

T CE = (p + ((\frac{a PR \cdot α}{({V m}^{2}) + (2 \cdot b PR \cdot V m) - ({b PR}^{2})}))) \cdot (\frac{V m - b PR}{[R]})

Go Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

T = ((P r \cdot P c) + ((\frac{a PR \cdot α}{({(V m,r \cdot V m,c)}^{2}) + (2 \cdot b PR \cdot (V m,r \cdot V m,c)) - ({b PR}^{2})}))) \cdot (\frac{(V m,r \cdot V m,c) - b PR}{[R]})

How to Evaluate Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters evaluator uses Pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))) to evaluate the Pressure, The Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the force that the gas exerts on the container boundaries. Pressure is denoted by p symbol.

How to evaluate Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters using this online evaluator? To use this online evaluator for Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters, enter Reduced Temperature (T_r), Critical Temperature (T_c), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Peng–Robinson Parameter b (b_PR), Peng–Robinson Parameter a (a_PR) & α-function (α) and hit the calculate button.

FAQs on Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

What is the formula to find Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

The formula of Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters is expressed as Pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))). Here is an example- 418.3093 = (([R]*(10*647))/((11.2*11.5)-0.12))-((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2))).

How to calculate Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

With Reduced Temperature (T_r), Critical Temperature (T_c), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c), Peng–Robinson Parameter b (b_PR), Peng–Robinson Parameter a (a_PR) & α-function (α) we can find Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters using the formula - Pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))). This formula also uses Universal gas constant .

What are the other ways to Calculate Pressure?

Here are the different ways to Calculate Pressure-

Pressure=(([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))
Pressure=Reduced Pressure*(0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a)
Pressure=Reduced Pressure*(0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b)

Can the Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters be negative?

Yes, the Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters, measured in Pressure can be negative.

Which unit is used to measure Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters is usually measured using the Pascal[Pa] for Pressure. Kilopascal[Pa], Bar[Pa], Pound Per Square Inch[Pa] are the few other units in which Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters can be measured.

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Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Formula

​GoPressure of Real Gas using Peng Robinson Equation Formula

​GoActual Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters Formula

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Example

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Solution

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Formula Elements

Other Formulas to find Pressure

Other formulas in Peng Robinson Model of Real Gas category

How to Evaluate Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

FAQs on Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

Variable Name

GoPressure of Real Gas using Peng Robinson Equation Formula

GoActual Pressure given Peng Robinson Parameter a, and other Actual and Reduced Parameters Formula