Isothermal Compression of Ideal Gas Calculator

✖Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight.ⓘ Number of Moles [N_moles]			+10% -10%
✖Temperature of Gas is the measure of hotness or coldness of a gas.ⓘ Temperature of Gas [T_g]			+10% -10%
✖Final Volume of System is the volume occupied by the molecules of the system when thermodynamic process has taken place.ⓘ Final Volume of System [V_f]			+10% -10%
✖Initial Volume of System is the volume occupied by the molecules of the sytem initially before the process has started.ⓘ Initial Volume of System [V_i]			+10% -10%

✖Isothermal Work is the Work done in the Isothermal process. In an isothermal process, the temperature remains constant.ⓘ Isothermal Compression of Ideal Gas [W_{Iso T}]

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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)
W_{Iso T} = N_moles*[R]*T_g*2.303*log10(V_f/V_i)
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

W_{Iso T} = N_moles*[R]*T_g*2.303*log10(V_f/V_i) --> 4*[R]*300*2.303*log10(13/11)

Evaluating ... ...

W_{Iso 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 00.020 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Ideal Gas Calculators

Isothermal Compression of Ideal Gas

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

Degree of Freedom given Molar Internal Energy of Ideal Gas

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

Ideal Gas Law for Calculating Volume

LaTeX Go Ideal Gas Law for Calculating Volume = [R]*Temperature of Gas/Total Pressure of Ideal Gas

Ideal Gas Law for Calculating Pressure

LaTeX Go Ideal Gas Law for Calculating Pressure = [R]*(Temperature of Gas)/Total Volume of System

< Basic Formulas of Thermodynamics Calculators

Total Number of Variables in System

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

Number of Components

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

Degree of Freedom

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

Number of Phases

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

Isothermal Compression of Ideal Gas Formula

LaTeX Go

Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System)
W_{Iso T} = N_moles*[R]*T_g*2.303*log10(V_f/V_i)

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 W_{Iso 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 (N_moles), Temperature of Gas (T_g), Final Volume of System (V_f) & Initial Volume of System (V_i) 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 W_{Iso T} = N_moles*[R]*T_g*2.303*log10(V_f/V_i) 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 (N_moles), Temperature of Gas (T_g), Final Volume of System (V_f) & Initial Volume of System (V_i). 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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