Isothermal Compression of Ideal Gas Solution

STEP 0: Pre-Calculation Summary
Formula Used
Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System)
WIso T = Nmoles*[R]*Tg*2.303*log10(Vf/Vi)
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 of Gas - (Measured in Kelvin) - Temperature of Gas is the measure of hotness or coldness of a gas.
Final Volume of System - (Measured in Cubic Meter) - Final Volume of System is the volume occupied by the molecules of the system when thermodynamic process has taken place.
Initial Volume of System - (Measured in Cubic Meter) - Initial Volume of System is the volume occupied by the molecules of the sytem initially before the process has started.
STEP 1: Convert Input(s) to Base Unit
Number of Moles: 4 --> No Conversion Required
Temperature of Gas: 300 Kelvin --> 300 Kelvin No Conversion Required
Final Volume of System: 13 Cubic Meter --> 13 Cubic Meter No Conversion Required
Initial Volume of System: 11 Cubic Meter --> 11 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
WIso T = Nmoles*[R]*Tg*2.303*log10(Vf/Vi) --> 4*[R]*300*2.303*log10(13/11)
Evaluating ... ...
WIso T = 1667.05826672037
STEP 3: Convert Result to Output's Unit
1667.05826672037 Joule --> No Conversion Required
FINAL ANSWER
1667.05826672037 1667.058 Joule <-- Isothermal Work
(Calculation completed in 00.004 seconds)

Credits

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Osmania University (OU), Hyderabad
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8 Ideal Gas Calculators

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)
Molar Internal Energy of Ideal Gas given Boltzmann Constant
Go Internal Energy = (Degree of Freedom*Number of Moles*[BoltZ]*Temperature of Gas)/2
Number of Moles given Internal Energy of Ideal Gas
Go Number of Moles = 2*Internal Energy/(Degree of Freedom*[BoltZ]*Temperature of Gas)
Temperature of Ideal Gas given its Internal Energy
Go Temperature of Gas = 2*Internal Energy/(Degree of Freedom*Number of Moles*[BoltZ])
Degree of Freedom given Molar Internal Energy of Ideal Gas
Go Degree of Freedom = 2*Internal Energy/(Number of Moles*[R]*Temperature of Gas)
Ideal Gas Law for Calculating Volume
Go Ideal Gas Law for Calculating Volume = [R]*Temperature of Gas/Total Pressure of Ideal Gas
Ideal Gas Law for Calculating Pressure
Go Ideal Gas Law for calculating Pressure = [R]*(Temperature of Gas)/Total Volume of System
Molar Internal Energy of Ideal Gas
Go Molar Internal Energy of Ideal gas = (Degree of Freedom*[R]*Temperature of Gas)/2

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 Compression of Ideal Gas Formula

Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System)
WIso T = Nmoles*[R]*Tg*2.303*log10(Vf/Vi)

Define Isothermal Process?

An isothermal process is a thermodynamic process in which the temperature of a system remains constant. The transfer of heat into or out of the system happens so slowly that thermal equilibrium is maintained.

How to Calculate Isothermal Compression of Ideal Gas?

Isothermal Compression of Ideal Gas calculator uses Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System) to calculate the Isothermal Work, The Isothermal Compression of Ideal Gas takes place when the heat of compression is removed during compression and when the temperature of the gas stays constant. Isothermal Work is denoted by WIso T symbol.

How to calculate Isothermal Compression of Ideal Gas using this online calculator? To use this online calculator for Isothermal Compression of Ideal Gas, enter Number of Moles (Nmoles), Temperature of Gas (Tg), Final Volume of System (Vf) & Initial Volume of System (Vi) and hit the calculate button. Here is how the Isothermal Compression of Ideal Gas calculation can be explained with given input values -> 1667.058 = 4*[R]*300*2.303*log10(13/11).

FAQ

What is Isothermal Compression of Ideal Gas?
The Isothermal Compression of Ideal Gas takes place when the heat of compression is removed during compression and when the temperature of the gas stays constant and is represented as WIso T = Nmoles*[R]*Tg*2.303*log10(Vf/Vi) or Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System). Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight, Temperature of Gas is the measure of hotness or coldness of a gas, Final Volume of System is the volume occupied by the molecules of the system when thermodynamic process has taken place & Initial Volume of System is the volume occupied by the molecules of the sytem initially before the process has started.
How to calculate Isothermal Compression of Ideal Gas?
The Isothermal Compression of Ideal Gas takes place when the heat of compression is removed during compression and when the temperature of the gas stays constant is calculated using Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System). To calculate Isothermal Compression of Ideal Gas, you need Number of Moles (Nmoles), Temperature of Gas (Tg), Final Volume of System (Vf) & Initial Volume of System (Vi). With our tool, you need to enter the respective value for Number of Moles, Temperature of Gas, Final Volume of System & Initial Volume of System 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 of Gas, Final Volume of System & Initial Volume of System. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Isothermal Work = Number of Moles*[R]*Temperature*2.303*log10(Final Volume of Gas/Initial Volume of Gas)
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