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

GoActual Temperature given Peng Robinson Parameter a, and other Reduced and Critical Parameters Formula

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

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Temperature is the degree or intensity of heat present in a substance or object. Check FAQs

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]})

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

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

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

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

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

0.1242 = ((3.7E-5 \cdot 218) + ((\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5)) - ({0.12}^{2})}))) \cdot (\frac{(11.2 \cdot 11.5) - 0.12}{8.3145})

0.1242K = ((3.7E-5 \cdot 218Pa) + ((\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})}))) \cdot (\frac{(11.2 \cdot 11.5m³/mol) - 0.12}{8.3145})

0.1242 = ((3.7E-5 \cdot 218) + ((\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5)) - ({0.12}^{2})}))) \cdot (\frac{(11.2 \cdot 11.5) - 0.12}{8.3145})

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

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

FIRST Step Consider the formula

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]})

Next Step Substitute values of Variables

∴

T = ((3.7E-5 \cdot 218Pa) + ((\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})}))) \cdot (\frac{(11.2 \cdot 11.5m³/mol) - 0.12}{[R]})

Next Step Substitute values of Constants

∴

T = ((3.7E-5 \cdot 218Pa) + ((\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})}))) \cdot (\frac{(11.2 \cdot 11.5m³/mol) - 0.12}{8.3145})

Next Step Prepare to Evaluate

∴

T = ((3.7E-5 \cdot 218) + ((\frac{0.1 \cdot 2}{({(11.2 \cdot 11.5)}^{2}) + (2 \cdot 0.12 \cdot (11.2 \cdot 11.5)) - ({0.12}^{2})}))) \cdot (\frac{(11.2 \cdot 11.5) - 0.12}{8.3145})

Next Step Evaluate

∴

T = 0.124177392063826K

LAST Step Rounding Answer

∴

T = 0.1242K

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

Variables

Constants

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Reduced Pressure

Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.

Symbol: P_r

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Reduced Pressure

Critical Pressure

Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.

Symbol: P_c

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Critical Pressure

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

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

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 Temperature

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

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

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

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

Other formulas in Peng Robinson Model of Real Gas category

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

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})})

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

Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters evaluator uses Temperature = ((Reduced Pressure*Critical Pressure)+(((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)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]) to evaluate the Temperature, The Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the degree or intensity of heat present in the volume of real gas. Temperature is denoted by T symbol.

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

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

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

The formula of Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters is expressed as Temperature = ((Reduced Pressure*Critical Pressure)+(((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)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]). Here is an example- 0.1241 = ((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R]).

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

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

What are the other ways to Calculate Temperature?

Here are the different ways to Calculate Temperature-

Temperature=Reduced Temperature*(sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2))))
Temperature=Reduced Temperature*(sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2))))
Temperature=Reduced Temperature*((Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R]))

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

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

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

Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters can be measured.

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

​GoActual Temperature given Peng Robinson Parameter a, and other Reduced and Critical Parameters Formula

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

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

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

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

Other Formulas to find Temperature

Other formulas in Peng Robinson Model of Real Gas category

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

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

Variable Name

GoActual Temperature given Peng Robinson Parameter a, and other Reduced and Critical Parameters Formula

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