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

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

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

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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. Check FAQs

T' c = \frac{((P r \cdot P' c) + (\frac{a}{({((V' m,r \cdot V m,c) + c)}^{2})})) \cdot (\frac{(V' m,r \cdot V m,c) - b'}{[R]})}{T r}

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

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

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

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

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

4.6E+6 = \frac{((0.8 \cdot 4.6E+6) + (\frac{0.1}{({((8.96 \cdot 11.5) + 0.0002)}^{2})})) \cdot (\frac{(8.96 \cdot 11.5) - 0.0024}{8.3145})}{10}

4.6E+6K = \frac{((0.8 \cdot 4.6E+6Pa) + (\frac{0.1}{({((8.96 \cdot 11.5m³/mol) + 0.0002)}^{2})})) \cdot (\frac{(8.96 \cdot 11.5m³/mol) - 0.0024}{8.3145})}{10}

4.6E+6 = \frac{((0.8 \cdot 4.6E+6) + (\frac{0.1}{({((8.96 \cdot 11.5) + 0.0002)}^{2})})) \cdot (\frac{(8.96 \cdot 11.5) - 0.0024}{8.3145})}{10}

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

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

FIRST Step Consider the formula

T' c = \frac{((P r \cdot P' c) + (\frac{a}{({((V' m,r \cdot V m,c) + c)}^{2})})) \cdot (\frac{(V' m,r \cdot V m,c) - b'}{[R]})}{T r}

Next Step Substitute values of Variables

∴

T' c = \frac{((0.8 \cdot 4.6E+6Pa) + (\frac{0.1}{({((8.96 \cdot 11.5m³/mol) + 0.0002)}^{2})})) \cdot (\frac{(8.96 \cdot 11.5m³/mol) - 0.0024}{[R]})}{10}

Next Step Substitute values of Constants

∴

T' c = \frac{((0.8 \cdot 4.6E+6Pa) + (\frac{0.1}{({((8.96 \cdot 11.5m³/mol) + 0.0002)}^{2})})) \cdot (\frac{(8.96 \cdot 11.5m³/mol) - 0.0024}{8.3145})}{10}

Next Step Prepare to Evaluate

∴

T' c = \frac{((0.8 \cdot 4.6E+6) + (\frac{0.1}{({((8.96 \cdot 11.5) + 0.0002)}^{2})})) \cdot (\frac{(8.96 \cdot 11.5) - 0.0024}{8.3145})}{10}

Next Step Evaluate

∴

T' c = 4560466.20226662K

LAST Step Rounding Answer

∴

T' c = 4.6E+6K

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

Variables

Constants

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 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 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

Clausius Parameter a

Clausius parameter a is an empirical parameter characteristic to equation obtained from Clausius model of real gas.

Symbol: a

Measurement: NAUnit: Unitless