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Work done per minute during Isothermal Compression is the energy transferred per minute during the isothermal compression of a gas in a single stage compressor. Check FAQs
WIsothermal=2.3⋅mgas⋅[R]⋅T1⋅ln(r)
WIsothermal - Work done per minute during Isothermal Compression?mgas - Mass of Gas?T1 - Temperature of Gas 1?r - Compression Ratio?[R] - Universal gas constant?

Work done during Isothermal Compression given Temperature and Compression Ratio Example

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With units
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Here is how the Work done during Isothermal Compression given Temperature and Compression Ratio equation looks like with Values.

Here is how the Work done during Isothermal Compression given Temperature and Compression Ratio equation looks like with Units.

Here is how the Work done during Isothermal Compression given Temperature and Compression Ratio equation looks like.

4814.0915Edit=2.3⋅716470Edit⋅8.3145⋅225.5Edit⋅ln(4.75Edit)
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Work done during Isothermal Compression given Temperature and Compression Ratio Solution

Follow our step by step solution on how to calculate Work done during Isothermal Compression given Temperature and Compression Ratio?

FIRST Step Consider the formula
WIsothermal=2.3⋅mgas⋅[R]⋅T1⋅ln(r)
Next Step Substitute values of Variables
∴ WIsothermal=2.3⋅716470g⋅[R]⋅225.5K⋅ln(4.75)
Next Step Substitute values of Constants
∴ WIsothermal=2.3⋅716470g⋅8.3145⋅225.5K⋅ln(4.75)
Next Step Convert Units
∴ WIsothermal=2.3⋅716.47kg⋅8.3145⋅225.5K⋅ln(4.75)
Next Step Prepare to Evaluate
∴ WIsothermal=2.3⋅716.47⋅8.3145⋅225.5⋅ln(4.75)
Next Step Evaluate
∴WIsothermal=4814091.51171515J
Next Step Convert to Output's Unit
∴WIsothermal=4814.09151171515KJ
LAST Step Rounding Answer
∴WIsothermal=4814.0915KJ

Work done during Isothermal Compression given Temperature and Compression Ratio Formula Elements

Variables
Constants
Functions
Work done per minute during Isothermal Compression
Work done per minute during Isothermal Compression is the energy transferred per minute during the isothermal compression of a gas in a single stage compressor.
Symbol: WIsothermal
Measurement: EnergyUnit: KJ
Note: Value can be positive or negative.
Formulas to find Work done per minute during Isothermal CompressionOpen Variable
Mass of Gas
Mass of Gas is the quantity of gas processed by a single stage compressor, typically measured in units of mass per unit time.
Symbol: mgas
Measurement: WeightUnit: g
Note: Value should be greater than 0.
Formulas to find Mass of GasOpen Variable
Temperature of Gas 1
Temperature of Gas 1 is the temperature of the gas at the inlet of the compressor in a single stage compression process.
Symbol: T1
Measurement: TemperatureUnit: K
Note: Value can be positive or negative.
Formulas to find Temperature of Gas 1Open Variable
Compression Ratio
Compression Ratio is the ratio of the volume of air or gas in a compressor at inlet to the volume at outlet in a single stage compression process.
Symbol: r
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Compression RatioOpen Variable
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
ln
The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.
Syntax: ln(Number)

Other Formulas to find Work done per minute during Isothermal Compression

​Go Work done during Isothermal Compression given Temperature and Volume Ratio
WIsothermal=2.3⋅m⋅[R]⋅T⋅ln(V1V2)
​Go Work done during Isothermal Compression given Temperature and Pressure Ratio
WIsothermal=2.3⋅m⋅[R]⋅T⋅ln(P2P1)
​Go Work done during Isothermal Compression given Pressure and Volume Ratio
WIsothermal=2.3⋅P1⋅V1⋅ln(V1V2)
​Go Work done during Isothermal Compression given Volume and Pressure Ratio
WIsothermal=2.3⋅P1⋅V1⋅ln(P2P1)

Other formulas in Work Done by Single Stage Compressor category

​Go Work done during polytropic compression
WPolytropic=(nn-1)⋅m⋅[R]⋅(Tdischarge-Trefrigerant)
​Go Work done during isentropic Compression given Specific Heat Capacity Constant Pressure
WIsentropic=m⋅Cp⋅(Tdischarge-Trefrigerant)
​Go Work done during isentropic compression
WIsentropic=(γγ-1)⋅m⋅[R]⋅(Tdischarge-Trefrigerant)

How to Evaluate Work done during Isothermal Compression given Temperature and Compression Ratio?

Work done during Isothermal Compression given Temperature and Compression Ratio evaluator uses Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio) to evaluate the Work done per minute during Isothermal Compression, Work done during Isothermal Compression given Temperature and Compression Ratio formula is defined as the energy transferred to the system during the compression process, where the temperature remains constant, and is a critical parameter in evaluating the performance of a single-stage compressor. Work done per minute during Isothermal Compression is denoted by WIsothermal symbol.

How to evaluate Work done during Isothermal Compression given Temperature and Compression Ratio using this online evaluator? To use this online evaluator for Work done during Isothermal Compression given Temperature and Compression Ratio, enter Mass of Gas (mgas), Temperature of Gas 1 (T1) & Compression Ratio (r) and hit the calculate button.

FAQs on Work done during Isothermal Compression given Temperature and Compression Ratio

What is the formula to find Work done during Isothermal Compression given Temperature and Compression Ratio?
The formula of Work done during Isothermal Compression given Temperature and Compression Ratio is expressed as Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio). Here is an example- 4.269704 = 2.3*716.47*[R]*225.5*ln(4.75).
How to calculate Work done during Isothermal Compression given Temperature and Compression Ratio?
With Mass of Gas (mgas), Temperature of Gas 1 (T1) & Compression Ratio (r) we can find Work done during Isothermal Compression given Temperature and Compression Ratio using the formula - Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio). This formula also uses Universal gas constant and Natural Logarithm (ln) function(s).
What are the other ways to Calculate Work done per minute during Isothermal Compression?
Here are the different ways to Calculate Work done per minute during Isothermal Compression-
  • Work done per minute during Isothermal Compression=2.3*Mass of Refrigerant in kg per minute*[R]*Temperature of Refrigerant*ln(Suction Volume/Discharge Volume)OpenImg
  • Work done per minute during Isothermal Compression=2.3*Mass of Refrigerant in kg per minute*[R]*Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction Pressure)OpenImg
  • Work done per minute during Isothermal Compression=2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume)OpenImg
Can the Work done during Isothermal Compression given Temperature and Compression Ratio be negative?
Yes, the Work done during Isothermal Compression given Temperature and Compression Ratio, measured in Energy can be negative.
Which unit is used to measure Work done during Isothermal Compression given Temperature and Compression Ratio?
Work done during Isothermal Compression given Temperature and Compression Ratio is usually measured using the Kilojoule[KJ] for Energy. Joule[KJ], Gigajoule[KJ], Megajoule[KJ] are the few other units in which Work done during Isothermal Compression given Temperature and Compression Ratio can be measured.
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