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Isothermal Compression of Ideal Gas Formula

GoIsothermal Work Done by Gas Formula

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Isothermal Work is the Work done in the Isothermal process. In an isothermal process, the temperature remains constant. Check FAQs

W Iso T = N moles \cdot [R] \cdot T g \cdot 2.303 \cdot \log 10 (\frac{V f}{V i})

W_{Iso T} - Isothermal Work?N_moles - Number of Moles?T_g - Temperature of Gas?V_f - Final Volume of System?V_i - Initial Volume of System?[R] - Universal gas constant?

Isothermal Compression of Ideal Gas Example

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Here is how the Isothermal Compression of Ideal Gas equation looks like with Values.

Here is how the Isothermal Compression of Ideal Gas equation looks like with Units.

Here is how the Isothermal Compression of Ideal Gas equation looks like.

1667.0583 = 4 \cdot 8.3145 \cdot 300 \cdot 2.303 \cdot \log 10 (\frac{13}{11})

1667.0583J = 4 \cdot 8.3145 \cdot 300K \cdot 2.303 \cdot \log 10 (\frac{13m³}{11m³})

1667.0583 = 4 \cdot 8.3145 \cdot 300 \cdot 2.303 \cdot \log 10 (\frac{13}{11})

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Isothermal Compression of Ideal Gas Solution

Follow our step by step solution on how to calculate Isothermal Compression of Ideal Gas?

FIRST Step Consider the formula

W Iso T = N moles \cdot [R] \cdot T g \cdot 2.303 \cdot \log 10 (\frac{V f}{V i})

Next Step Substitute values of Variables

∴

W Iso T = 4 \cdot [R] \cdot 300K \cdot 2.303 \cdot \log 10 (\frac{13m³}{11m³})

Next Step Substitute values of Constants

∴

W Iso T = 4 \cdot 8.3145 \cdot 300K \cdot 2.303 \cdot \log 10 (\frac{13m³}{11m³})

Next Step Prepare to Evaluate

∴

W Iso T = 4 \cdot 8.3145 \cdot 300 \cdot 2.303 \cdot \log 10 (\frac{13}{11})

Next Step Evaluate

∴

W Iso T = 1667.05826672037J

LAST Step Rounding Answer

∴

W Iso T = 1667.0583J

Isothermal Compression of Ideal Gas Formula Elements

Variables

Constants

Functions

Isothermal Work

Isothermal Work is the Work done in the Isothermal process. In an isothermal process, the temperature remains constant.

Symbol: W_{Iso T}

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Isothermal Work

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.

Symbol: N_moles

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Moles

Temperature of Gas

Temperature of Gas is the measure of hotness or coldness of a gas.

Symbol: T_g

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature of Gas

Final Volume of System

Final Volume of System is the volume occupied by the molecules of the system when thermodynamic process has taken place.

Symbol: V_f

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Final Volume of System

Initial Volume of System

Initial Volume of System is the volume occupied by the molecules of the sytem initially before the process has started.

Symbol: V_i

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Formulas to find Initial Volume of System

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

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.

Syntax: log10(Number)

Other Formulas to find Isothermal Work

Go Isothermal Work Done by Gas

W Iso T = N moles \cdot [R] \cdot T \cdot 2.303 \cdot \log 10 (\frac{V 2}{V 1})

Other formulas in Ideal Gas category

Go Degree of Freedom

F = C - p + 2

Go Number of Components

C = F + p - 2

Go Number of Phases

p = C - F + 2

Go Total Number of Variables in System

T v = p \cdot (C - 1) + 2

How to Evaluate Isothermal Compression of Ideal Gas?

Isothermal Compression of Ideal Gas evaluator uses Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System) to evaluate 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 evaluate Isothermal Compression of Ideal Gas using this online evaluator? To use this online evaluator 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.

FAQs on Isothermal Compression of Ideal Gas

What is the formula to find Isothermal Compression of Ideal Gas?

The formula of Isothermal Compression of Ideal Gas is expressed as Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System). Here is an example- 1667.058 = 4*[R]*300*2.303*log10(13/11).

How to calculate Isothermal Compression of Ideal Gas?

With Number of Moles (N_moles), Temperature of Gas (T_g), Final Volume of System (V_f) & Initial Volume of System (V_i) we can find Isothermal Compression of Ideal Gas using the formula - Isothermal Work = Number of Moles*[R]*Temperature of Gas*2.303*log10(Final Volume of System/Initial Volume of System). This formula also uses Universal gas constant and Common Logarithm (log10) function(s).

What are the other ways to Calculate Isothermal Work?

Here are the different ways to Calculate Isothermal Work-

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

Can the Isothermal Compression of Ideal Gas be negative?

Yes, the Isothermal Compression of Ideal Gas, measured in Energy can be negative.

Which unit is used to measure Isothermal Compression of Ideal Gas?

Isothermal Compression of Ideal Gas is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Isothermal Compression of Ideal Gas can be measured.

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Isothermal Compression of Ideal Gas Formula

​GoIsothermal Work Done by Gas Formula

Isothermal Compression of Ideal Gas Example

Isothermal Compression of Ideal Gas Solution

Isothermal Compression of Ideal Gas Formula Elements

Other Formulas to find Isothermal Work

Other formulas in Ideal Gas category

How to Evaluate Isothermal Compression of Ideal Gas?

FAQs on Isothermal Compression of Ideal Gas

Variable Name

GoIsothermal Work Done by Gas Formula