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Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters Formula

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

GoCritical Pressure of Real Gas using Peng Robinson Equation given Peng Robinson Parameter a Formula

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

P c = \frac{(\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 r}

P_c - Critical 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?P_r - Reduced Pressure?[R] - Universal gas constant?

Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters Example

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

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

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

1.1E+7 = \frac{(\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})})}{3.7E-5}

1.1E+7Pa = \frac{(\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})})}{3.7E-5}

1.1E+7 = \frac{(\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})})}{3.7E-5}

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Critical Pressure using Peng Robinson Equation given Reduced and Critical Parameters Solution

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

FIRST Step Consider the formula

P c = \frac{(\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 r}

Next Step Substitute values of Variables

∴

P c = \frac{(\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})})}{3.7E-5}

Next Step Substitute values of Constants

∴

P c = \frac{(\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})})}{3.7E-5}

Next Step Prepare to Evaluate

∴

P c = \frac{(\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})})}{3.7E-5}

Next Step Evaluate

∴

P c = 11375488.5485034Pa

LAST Step Rounding Answer

∴

P c = 1.1E+7Pa

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

Variables

Constants

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

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