Isothermal Work using Pressure Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System)
WT(Pressure Ratio) = Pi*V1*ln(Pi/Pf)
This formula uses 1 Functions, 4 Variables
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
Variables Used
Isothermal Work given Pressure Ratio - (Measured in Joule) - Isothermal Work given Pressure Ratio is the energy transferred to or from an object via the application of force along with a displacement for a system whose temperature is constant.
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.
Final Pressure of System - (Measured in Pascal) - Final Pressure of System is the total final pressure exerted by the molecules inside the system.
STEP 1: Convert Input(s) to Base Unit
Initial Pressure of System: 65 Pascal --> 65 Pascal No Conversion Required
Initial Volume of Gas: 50 Cubic Meter --> 50 Cubic Meter No Conversion Required
Final Pressure of System: 18.43 Pascal --> 18.43 Pascal No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
WT(Pressure Ratio) = Pi*V1*ln(Pi/Pf) --> 65*50*ln(65/18.43)
Evaluating ... ...
WT(Pressure Ratio) = 4096.32436919519
STEP 3: Convert Result to Output's Unit
4096.32436919519 Joule --> No Conversion Required
FINAL ANSWER
4096.32436919519 4096.324 Joule <-- Isothermal Work given Pressure Ratio
(Calculation completed in 00.004 seconds)

Credits

Created by Suman Ray Pramanik
Indian Institute of Technology (IIT), Kanpur
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6 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 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

Isothermal Work using Pressure Ratio Formula

Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System)
WT(Pressure Ratio) = Pi*V1*ln(Pi/Pf)

What is Isothermal Work?

Isothermal work is the energy transferred to or from an object via the application of force along with a displacement for a system whose temperature is constant. Given the value of volume at point 1 and the respective pressures, the isothermal work can be calculated. Positive work adds energy to a system. Negative work removes or dissipates energy from the system.

How to Calculate Isothermal Work using Pressure Ratio?

Isothermal Work using Pressure Ratio calculator uses Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System) to calculate the Isothermal Work given Pressure Ratio, Isothermal Work using Pressure Ratio is the energy transferred to or from an object via the application of force along with a displacement for a system whose temperature is constant. Isothermal Work given Pressure Ratio is denoted by WT(Pressure Ratio) symbol.

How to calculate Isothermal Work using Pressure Ratio using this online calculator? To use this online calculator for Isothermal Work using Pressure Ratio, enter Initial Pressure of System (Pi), Initial Volume of Gas (V1) & Final Pressure of System (Pf) and hit the calculate button. Here is how the Isothermal Work using Pressure Ratio calculation can be explained with given input values -> 4096.324 = 65*50*ln(65/18.43).

FAQ

What is Isothermal Work using Pressure Ratio?
Isothermal Work using Pressure Ratio is the energy transferred to or from an object via the application of force along with a displacement for a system whose temperature is constant and is represented as WT(Pressure Ratio) = Pi*V1*ln(Pi/Pf) or Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System). 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 & Final Pressure of System is the total final pressure exerted by the molecules inside the system.
How to calculate Isothermal Work using Pressure Ratio?
Isothermal Work using Pressure Ratio is the energy transferred to or from an object via the application of force along with a displacement for a system whose temperature is constant is calculated using Isothermal Work given Pressure Ratio = Initial Pressure of System*Initial Volume of Gas*ln(Initial Pressure of System/Final Pressure of System). To calculate Isothermal Work using Pressure Ratio, you need Initial Pressure of System (Pi), Initial Volume of Gas (V1) & Final Pressure of System (Pf). With our tool, you need to enter the respective value for Initial Pressure of System, Initial Volume of Gas & Final Pressure of System 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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