Isothermal Work using Pressure Ratio Calculator

✖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%
✖Final Pressure of System is the total final pressure exerted by the molecules inside the system.ⓘ Final Pressure of System [P_f]			+10% -10%

✖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.ⓘ Isothermal Work using Pressure Ratio [W_{T(Pressure Ratio)}]

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Formula

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Isothermal Work using Pressure Ratio

Formula

W T(Pressure Ratio) = P i \cdot V 1 \cdot \ln (\frac{P i}{P f})

Example

4096.324 J = 65 Pa \cdot 50 m³ \cdot \ln (\frac{65 Pa}{18.43 Pa})

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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)
W_{T(Pressure Ratio)} = P_i*V₁*ln(P_i/P_f)
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

W_{T(Pressure Ratio)} = P_i*V₁*ln(P_i/P_f) --> 65*50*ln(65/18.43)

Evaluating ... ...

W_{T(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)

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Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

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< 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)

Work Done in Isobaric Process

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

< Basic Formulas of Thermodynamics Calculators

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)
W_{T(Pressure Ratio)} = P_i*V₁*ln(P_i/P_f)

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 W_{T(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 (P_i), Initial Volume of Gas (V₁) & Final Pressure of System (P_f) 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 W_{T(Pressure Ratio)} = P_i*V₁*ln(P_i/P_f) 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 (P_i), Initial Volume of Gas (V₁) & Final Pressure of System (P_f). 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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