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

GoCritical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter Formula

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

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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. Check FAQs

T c = \frac{((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 r}

T_c - Critical 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?T_r - Reduced Temperature?[R] - Universal gas constant?

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

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

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

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

0.0124 = \frac{((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})}{10}

0.0124K = \frac{((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})}{10}

0.0124 = \frac{((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})}{10}

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

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

FIRST Step Consider the formula

T c = \frac{((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 r}

Next Step Substitute values of Variables

∴

T c = \frac{((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]})}{10}

Next Step Substitute values of Constants

∴

T c = \frac{((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})}{10}

Next Step Prepare to Evaluate

∴

T c = \frac{((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})}{10}

Next Step Evaluate

∴

T c = 0.0124177392063826K

LAST Step Rounding Answer

∴

T c = 0.0124K

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

Variables

Constants

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 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