Isothermal Work Done by Gas Solution

STEP 0: Pre-Calculation Summary
Formula Used
Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas)
WIso T = Nmoles*[R]*T*2.303*log10(V2/V1)
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Functions Used
log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)
Variables Used
Isothermal Work - (Measured in Joule) - Isothermal Work is the Work done in the Isothermal process. In an isothermal process, the temperature remains constant.
Number of Moles - Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
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 Volume of Gas - (Measured in Cubic Meter) - Initial Volume of Gas is defined as the volume of gas at the beginning of the process.
STEP 1: Convert Input(s) to Base Unit
Number of Moles: 4 --> No Conversion Required
Temperature: 288.16 Kelvin --> 288.16 Kelvin No Conversion Required
Final Volume of Gas: 99 Cubic Meter --> 99 Cubic Meter No Conversion Required
Initial Volume of Gas: 50 Cubic Meter --> 50 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
WIso T = Nmoles*[R]*T*2.303*log10(V2/V1) --> 4*[R]*288.16*2.303*log10(99/50)
Evaluating ... ...
WIso T = 6547.69438489809
STEP 3: Convert Result to Output's Unit
6547.69438489809 Joule --> No Conversion Required
FINAL ANSWER
6547.69438489809 6547.694 Joule <-- Isothermal Work
(Calculation completed in 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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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 Done by Gas Formula

Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas)
WIso T = Nmoles*[R]*T*2.303*log10(V2/V1)

Define Isothermal Process?

In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature of the system remains constant: ΔT = 0. ... In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).

How to Calculate Isothermal Work Done by Gas?

Isothermal Work Done by Gas calculator uses Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas) to calculate the Isothermal Work, Isothermal Work Done by Gas is defined as the work done at a constant temperature. The internal energy of the closed undergoing isothermal process is constant. Isothermal Work is denoted by WIso T symbol.

How to calculate Isothermal Work Done by Gas using this online calculator? To use this online calculator for Isothermal Work Done by Gas, enter Number of Moles (Nmoles), Temperature (T), Final Volume of Gas (V2) & Initial Volume of Gas (V1) and hit the calculate button. Here is how the Isothermal Work Done by Gas calculation can be explained with given input values -> 6547.694 = 4*[R]*288.16*2.303*log10(99/50).

FAQ

What is Isothermal Work Done by Gas?
Isothermal Work Done by Gas is defined as the work done at a constant temperature. The internal energy of the closed undergoing isothermal process is constant and is represented as WIso T = Nmoles*[R]*T*2.303*log10(V2/V1) or Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas). Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight, Temperature is the degree or intensity of heat present in a substance or object, Final Volume of Gas is defined as the volume of gas at the end of the process & Initial Volume of Gas is defined as the volume of gas at the beginning of the process.
How to calculate Isothermal Work Done by Gas?
Isothermal Work Done by Gas is defined as the work done at a constant temperature. The internal energy of the closed undergoing isothermal process is constant is calculated using Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas). To calculate Isothermal Work Done by Gas, you need Number of Moles (Nmoles), Temperature (T), Final Volume of Gas (V2) & Initial Volume of Gas (V1). With our tool, you need to enter the respective value for Number of Moles, Temperature, Final Volume of Gas & Initial Volume of Gas 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 Isothermal Work?
In this formula, Isothermal Work uses Number of Moles, Temperature, Final Volume of Gas & Initial Volume of Gas. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System)
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