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

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

T r = \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 c}

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

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

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

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

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

0.0002 = \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})}{647}

0.0002 = \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})}{647K}

0.0002 = \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})}{647}

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

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

FIRST Step Consider the formula

T r = \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 c}

Next Step Substitute values of Variables

∴

T r = \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]})}{647K}

Next Step Substitute values of Constants

∴

T r = \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})}{647K}

Next Step Prepare to Evaluate

∴

T r = \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})}{647}

Next Step Evaluate

∴

T r = 0.000191927963004368

LAST Step Rounding Answer

∴

T r = 0.0002

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

Variables

Constants

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

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