Polytropic Work Calculator

✖Final Pressure of System is the total final pressure exerted by the molecules inside the system.ⓘ Final Pressure of System [P_f]			+10% -10%
✖Final Volume of Gas is defined as the volume of gas at the end of the process.ⓘ Final Volume of Gas [V₂]			+10% -10%
✖Initial Pressure of System is the total initial pressure exerted by the molecules inside the system.ⓘ Initial Pressure of System [P_i]			+10% -10%
✖Initial Volume of Gas is defined as the volume of gas at the beginning of the process.ⓘ Initial Volume of Gas [V₁]			+10% -10%
✖The Polytropic Index is that defined via a polytropic equation of state. The index dictates the type of thermodynamic process.ⓘ Polytropic Index [n]			+10% -10%

✖Polytropic Work is the energy transferred to or from an object via the application of force along with a displacement for a system whose pressure and volume obey a certain thermodynamic relation.ⓘ Polytropic Work [W_polytropic]

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Formula

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Polytropic Work

Formula

`"W"_{"polytropic"} = ("P"_{"f"}*"V"_{"2"}-"P"_{"i"}*"V"_{"1"})/(1-"n")`

Example

`"4751.433J"=("18.43Pa"*"99m³"-"65Pa"*"50m³")/(1-"1.30")`

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Polytropic Work Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index)
W_polytropic = (P_f*V₂-P_i*V₁)/(1-n)
This formula uses 6 Variables

Variables Used

Polytropic Work - (Measured in Joule) - Polytropic Work is the energy transferred to or from an object via the application of force along with a displacement for a system whose pressure and volume obey a certain thermodynamic relation.
Final Pressure of System - (Measured in Pascal) - Final Pressure of System is the total final pressure exerted by the molecules inside the system.
Final Volume of Gas - (Measured in Cubic Meter) - Final Volume of Gas is defined as the volume of gas at the end of the process.
Initial Pressure of System - (Measured in Pascal) - Initial Pressure of System is the total initial pressure exerted by the molecules inside the system.
Initial Volume of Gas - (Measured in Cubic Meter) - Initial Volume of Gas is defined as the volume of gas at the beginning of the process.
Polytropic Index - The Polytropic Index is that defined via a polytropic equation of state. The index dictates the type of thermodynamic process.

STEP 1: Convert Input(s) to Base Unit

Final Pressure of System: 18.43 Pascal --> 18.43 Pascal No Conversion Required
Final Volume of Gas: 99 Cubic Meter --> 99 Cubic Meter No Conversion Required
Initial Pressure of System: 65 Pascal --> 65 Pascal No Conversion Required
Initial Volume of Gas: 50 Cubic Meter --> 50 Cubic Meter No Conversion Required
Polytropic Index: 1.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_polytropic = (P_f*V₂-P_i*V₁)/(1-n) --> (18.43*99-65*50)/(1-1.3)

Evaluating ... ...

W_polytropic = 4751.43333333333

STEP 3: Convert Result to Output's Unit

4751.43333333333 Joule --> No Conversion Required

FINAL ANSWER

4751.43333333333 ≈ 4751.433 Joule <-- Polytropic Work

(Calculation completed in 00.004 seconds)

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Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

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< 9 Closed System Work Calculators

Isothermal Work using Pressure Ratio

Go Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System)

Isothermal Work Done by Gas

Go Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas)

Polytropic Work

Go Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index)

Isothermal Work using Volume Ratio

Go Isothermal Work given Volume Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Final Volume of Gas/Initial Volume of Gas)

Isothermal Work using Temperature

Go Isothermal work given temperature = [R]*Temperature*ln(Initial Pressure of System/Final Pressure of System)

Work Done in Adiabatic Process given Adiabatic Index

Go Work = (Mass of Gas*[R]*(Initial Temperature-Final Temperature))/(Heat Capacity Ratio-1)

Isobaric Work for given Mass and Temperatures

Go Isobaric Work = Amount of Gaseous Substance in Moles*[R]*(Final Temperature-Initial Temperature)

Isobaric Work for given Pressure and Volumes

Go Isobaric Work = Absolute Pressure*(Final Volume of System-Initial Volume of System)

Work Done in Isobaric Process

Go Isobaric Work = Pressure Object*(Final Volume of Gas-Initial Volume of Gas)

< 16 Basic Formulas of Thermodynamics Calculators

Work Done in Adiabatic Process using Specific Heat Capacity at Constant Pressure and Volume

Go Work done in Thermodynamic Process = (Initial Pressure of System*Initial Volume of System-Final Pressure of System*Final Volume of System)/((Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume)-1)

Liquid phase mole fraction using Gamma - phi formulation of VLE

Go Mole Fraction of Component in Liquid Phase = (Mole Fraction of Component in Vapor Phase*Fugacity Coefficient*Total Pressure)/(Activity Coefficient*Saturated Pressure)

Isothermal Compression of Ideal Gas

Go Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System)

Isothermal Work using Pressure Ratio

Go Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System)

Isothermal Work Done by Gas

Go Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas)

Polytropic Work

Go Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index)

Isothermal Work using Volume Ratio

Go Isothermal Work given Volume Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Final Volume of Gas/Initial Volume of Gas)

Isothermal Work using Temperature

Go Isothermal work given temperature = [R]*Temperature*ln(Initial Pressure of System/Final Pressure of System)

Compressibility Factor

Go Compressibility Factor = (Pressure Object*Specific Volume)/(Specific Gas Constant*Temperature)

Degree of Freedom given Molar Internal Energy of Ideal Gas

Go Degree of Freedom = 2*Internal Energy/(Number of Moles*[R]*Temperature of Gas)

Degree of Freedom given Equipartition Energy

Go Degree of Freedom = 2*Equipartition Energy/([BoltZ]*Temperature of Gas B)

Work Done in Isobaric Process

Go Isobaric Work = Pressure Object*(Final Volume of Gas-Initial Volume of Gas)

Total Number of Variables in System

Go Total Number of Variables in System = Number of Phases*(Number of Components in System-1)+2

Number of Components

Go Number of Components in System = Degree of Freedom+Number of Phases-2

Degree of Freedom

Go Degree of Freedom = Number of Components in System-Number of Phases+2

Number of Phases

Go Number of Phases = Number of Components in System-Degree of Freedom+2

Polytropic Work Formula

Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index)
W_polytropic = (P_f*V₂-P_i*V₁)/(1-n)

What is Polytropic Work?

Polytropic work is the energy transferred to or from an object via the application of force along with a displacement for a system whose pressure and volume obey a certain thermodynamic relation. For a polytropic process path, one in which pVⁿ=constant along the path, n is the polytropic index. Such a process path is typically regarded as reversible, and the temperature, volume, and pressure can be varying along the path. Positive work adds energy to a system. Negative work removes or dissipates energy from the system.

How to Calculate Polytropic Work?

Polytropic Work calculator uses Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index) to calculate the Polytropic Work, Polytropic Work is the energy transferred to or from an object via the application of force along with a displacement for a system whose pressure and volume obey a certain thermodynamic relation. Polytropic Work is denoted by W_polytropic symbol.

How to calculate Polytropic Work using this online calculator? To use this online calculator for Polytropic Work, enter Final Pressure of System (P_f), Final Volume of Gas (V₂), Initial Pressure of System (P_i), Initial Volume of Gas (V₁) & Polytropic Index (n) and hit the calculate button. Here is how the Polytropic Work calculation can be explained with given input values -> 4751.433 = (18.43*99-65*50)/(1-1.3).

FAQ

What is Polytropic Work?

Polytropic Work is the energy transferred to or from an object via the application of force along with a displacement for a system whose pressure and volume obey a certain thermodynamic relation and is represented as W_polytropic = (P_f*V₂-P_i*V₁)/(1-n) or Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index). Final Pressure of System is the total final pressure exerted by the molecules inside the system, Final Volume of Gas is defined as the volume of gas at the end of the process, Initial Pressure of System is the total initial pressure exerted by the molecules inside the system, Initial Volume of Gas is defined as the volume of gas at the beginning of the process & The Polytropic Index is that defined via a polytropic equation of state. The index dictates the type of thermodynamic process.

How to calculate Polytropic Work?

Polytropic Work is the energy transferred to or from an object via the application of force along with a displacement for a system whose pressure and volume obey a certain thermodynamic relation is calculated using Polytropic Work = (Final Pressure of System*Final Volume of Gas-Initial Pressure of System*Initial Volume of Gas)/(1-Polytropic Index). To calculate Polytropic Work, you need Final Pressure of System (P_f), Final Volume of Gas (V₂), Initial Pressure of System (P_i), Initial Volume of Gas (V₁) & Polytropic Index (n). With our tool, you need to enter the respective value for Final Pressure of System, Final Volume of Gas, Initial Pressure of System, Initial Volume of Gas & Polytropic Index and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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