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Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
reduced_temperature = Temperature/(sqrt((Peng–Robinson parameter a*Critical Pressure)/(0.45724*([R]^2))))
Tr = T/(sqrt((a*Pc)/(0.45724*([R]^2))))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Temperature - Temperature is the degree or intensity of heat present in a substance or object. (Measured in Kelvin)
Peng–Robinson parameter a- Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Critical Pressure - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature. (Measured in Pascal)
STEP 1: Convert Input(s) to Base Unit
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Peng–Robinson parameter a: 0.1 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tr = T/(sqrt((a*Pc)/(0.45724*([R]^2)))) --> 85/(sqrt((0.1*218)/(0.45724*([R]^2))))
Evaluating ... ...
Tr = 102.35215051138
STEP 3: Convert Result to Output's Unit
102.35215051138 --> No Conversion Required
FINAL ANSWER
102.35215051138 <-- Reduced Temperature
(Calculation completed in 00.000 seconds)

10+ Peng–Robinson model of Real Gas Calculators

Peng–Robinson α-function using Peng–Robinson equation in terms of reduced and critical parameters
alpha_function = ((([R]*(Critical Temperature*Reduced Temperature))/((Critical Molar Volume*Reduced Molar Volume)-Peng–Robinson parameter b))-(Critical Pressure*Reduced Pressure))*(((Critical Molar Volume*Reduced Molar Volume)^2)+(2*Peng–Robinson parameter b*(Critical Molar Volume*Reduced Molar Volume))-(Peng–Robinson parameter b^2))/Peng–Robinson parameter a Go
Critical Pressure using Peng–Robinson equation in terms of reduced and critical parameters
critical_pressure = ((([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))))/Reduced Pressure Go
Peng–Robinson parameter a using Peng–Robinson equation in terms of reduced and critical parameters
peng_robinson_parameter_a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))/α-function Go
Pressure of real gas using Peng–Robinson equation in terms of reduced and critical parameters
pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))) Go
Temperature of real gas using Peng–Robinson equation in terms of reduced and critical parameters
temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b)/[R]) Go
Critical Pressure of real gas using Peng–Robinson equation in terms of reduced and actual parameters
critical_pressure = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))))/Reduced Pressure Go
Peng–Robinson α-function using Peng–Robinson equation
alpha_function = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/Peng–Robinson parameter a Go
Temperature of real gas using Peng–Robinson equation
temperature = (Pressure+(((Peng–Robinson parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2)))))*((Molar Volume-Peng–Robinson parameter b)/[R]) Go
Pressure of real gas using Peng–Robinson equation
pressure = (([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))) Go
Peng–Robinson parameter a using Peng–Robinson equation
peng_robinson_parameter_a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/α-function Go

Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters Formula

reduced_temperature = Temperature/(sqrt((Peng–Robinson parameter a*Critical Pressure)/(0.45724*([R]^2))))
Tr = T/(sqrt((a*Pc)/(0.45724*([R]^2))))

What are Real Gases?

Real gases are non ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behavior of real gases, the following must be taken into account: - compressibility effects; - variable specific heat capacity; - van der Waals forces; - non-equilibrium thermodynamic effects; - issues with molecular dissociation and elementary reactions with variable composition.

How to Calculate Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters?

Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters calculator uses reduced_temperature = Temperature/(sqrt((Peng–Robinson parameter a*Critical Pressure)/(0.45724*([R]^2)))) to calculate the Reduced Temperature, The Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters formula is defined as the actual temperature of the fluid to its critical temperature. It is dimensionless. Reduced Temperature and is denoted by Tr symbol.

How to calculate Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters using this online calculator? To use this online calculator for Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters, enter Temperature (T), Peng–Robinson parameter a (a) and Critical Pressure (Pc) and hit the calculate button. Here is how the Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters calculation can be explained with given input values -> 102.3522 = 85/(sqrt((0.1*218)/(0.45724*([R]^2)))).

FAQ

What is Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters?
The Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters formula is defined as the actual temperature of the fluid to its critical temperature. It is dimensionless and is represented as Tr = T/(sqrt((a*Pc)/(0.45724*([R]^2)))) or reduced_temperature = Temperature/(sqrt((Peng–Robinson parameter a*Critical Pressure)/(0.45724*([R]^2)))). Temperature is the degree or intensity of heat present in a substance or object, Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas and Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
How to calculate Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters?
The Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters formula is defined as the actual temperature of the fluid to its critical temperature. It is dimensionless is calculated using reduced_temperature = Temperature/(sqrt((Peng–Robinson parameter a*Critical Pressure)/(0.45724*([R]^2)))). To calculate Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters, you need Temperature (T), Peng–Robinson parameter a (a) and Critical Pressure (Pc). With our tool, you need to enter the respective value for Temperature, Peng–Robinson parameter a and Critical Pressure and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Reduced Temperature?
In this formula, Reduced Temperature uses Temperature, Peng–Robinson parameter a and Critical Pressure. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • pressure = (([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2)))
  • pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2)))
  • temperature = (Pressure+(((Peng–Robinson parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2)))))*((Molar Volume-Peng–Robinson parameter b)/[R])
  • temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b)/[R])
  • peng_robinson_parameter_a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/α-function
  • peng_robinson_parameter_a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))/α-function
  • alpha_function = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))/Peng–Robinson parameter a
  • alpha_function = ((([R]*(Critical Temperature*Reduced Temperature))/((Critical Molar Volume*Reduced Molar Volume)-Peng–Robinson parameter b))-(Critical Pressure*Reduced Pressure))*(((Critical Molar Volume*Reduced Molar Volume)^2)+(2*Peng–Robinson parameter b*(Critical Molar Volume*Reduced Molar Volume))-(Peng–Robinson parameter b^2))/Peng–Robinson parameter a
  • critical_pressure = ((([R]*Temperature)/(Molar Volume-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson parameter b*Molar Volume)-(Peng–Robinson parameter b^2))))/Reduced Pressure
  • critical_pressure = ((([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson parameter b))-((Peng–Robinson parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson parameter b^2))))/Reduced Pressure
Where is the Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters calculator used?
Among many, Reduced Temperature in terms of Peng–Robinson parameter a and other actual & critical parameters calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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