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

GoCritical Pressure of Real Gas using Clausius Equation given Actual and Critical Parameters Formula

GoCritical Pressure of Real Gas using Clausius Equation given Reduced and Actual Parameters Formula

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Critical Pressure of Real Gas 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'}) - (\frac{a}{(T r \cdot T' c) \cdot ({((V' m,r \cdot V m,c) + c)}^{2})})}{P r}

P'_c - Critical Pressure of Real Gas?T_r - Reduced Temperature?T'_c - Critical Temperature For Clausius Model?V'_m,r - Reduced Molar Volume for Real Gas?V_m,c - Critical Molar Volume?b' - Clausius Parameter b for Real Gas?a - Clausius Parameter a?c - Clausius Parameter c?P_r - Reduced Pressure?[R] - Universal gas constant?

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

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

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

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

155.7385 = \frac{(\frac{8.3145 \cdot (10 \cdot 154.4)}{(8.96 \cdot 11.5) - 0.0024}) - (\frac{0.1}{(10 \cdot 154.4) \cdot ({((8.96 \cdot 11.5) + 0.0002)}^{2})})}{0.8}

155.7385Pa = \frac{(\frac{8.3145 \cdot (10 \cdot 154.4K)}{(8.96 \cdot 11.5m³/mol) - 0.0024}) - (\frac{0.1}{(10 \cdot 154.4K) \cdot ({((8.96 \cdot 11.5m³/mol) + 0.0002)}^{2})})}{0.8}

155.7385 = \frac{(\frac{8.3145 \cdot (10 \cdot 154.4)}{(8.96 \cdot 11.5) - 0.0024}) - (\frac{0.1}{(10 \cdot 154.4) \cdot ({((8.96 \cdot 11.5) + 0.0002)}^{2})})}{0.8}

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

Follow our step by step solution on how to calculate Critical Pressure of Real Gas using Clausius 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'}) - (\frac{a}{(T r \cdot T' c) \cdot ({((V' m,r \cdot V m,c) + c)}^{2})})}{P r}

Next Step Substitute values of Variables

∴

P' c = \frac{(\frac{[R] \cdot (10 \cdot 154.4K)}{(8.96 \cdot 11.5m³/mol) - 0.0024}) - (\frac{0.1}{(10 \cdot 154.4K) \cdot ({((8.96 \cdot 11.5m³/mol) + 0.0002)}^{2})})}{0.8}

Next Step Substitute values of Constants

∴

P' c = \frac{(\frac{8.3145 \cdot (10 \cdot 154.4K)}{(8.96 \cdot 11.5m³/mol) - 0.0024}) - (\frac{0.1}{(10 \cdot 154.4K) \cdot ({((8.96 \cdot 11.5m³/mol) + 0.0002)}^{2})})}{0.8}

Next Step Prepare to Evaluate

∴

P' c = \frac{(\frac{8.3145 \cdot (10 \cdot 154.4)}{(8.96 \cdot 11.5) - 0.0024}) - (\frac{0.1}{(10 \cdot 154.4) \cdot ({((8.96 \cdot 11.5) + 0.0002)}^{2})})}{0.8}

Next Step Evaluate

∴

P' c = 155.738463671553Pa

LAST Step Rounding Answer

∴

P' c = 155.7385Pa

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

Variables

Constants

Critical Pressure of Real Gas

Critical Pressure of Real Gas 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 of Real Gas

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 For Clausius Model

Critical Temperature For Clausius Model is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, 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 For Clausius Model

Reduced Molar Volume for Real Gas

Reduced Molar Volume for Real Gas 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