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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⋅m⋅[R]⋅T⋅ln(V1V2)
WIsothermal - Work done per minute during Isothermal Compression?m - Mass of Refrigerant in kg per minute?T - Temperature of Refrigerant?V1 - Suction Volume?V2 - Discharge Volume?[R] - Universal gas constant?

Work done during Isothermal Compression given Temperature and Volume Ratio Example

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

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

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

4814.6961Edit=2.3⋅200Edit⋅8.3145⋅36550Edit⋅ln(10Edit1.2663Edit)
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Work done during Isothermal Compression given Temperature and Volume Ratio Solution

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

FIRST Step Consider the formula
WIsothermal=2.3⋅m⋅[R]⋅T⋅ln(V1V2)
Next Step Substitute values of Variables
∴ WIsothermal=2.3⋅200kg/min⋅[R]⋅36550K⋅ln(10m³1.2663m³)
Next Step Substitute values of Constants
∴ WIsothermal=2.3⋅200kg/min⋅8.3145⋅36550K⋅ln(10m³1.2663m³)
Next Step Convert Units
∴ WIsothermal=2.3⋅3.3333kg/s⋅8.3145⋅36550K⋅ln(10m³1.2663m³)
Next Step Prepare to Evaluate
∴ WIsothermal=2.3⋅3.3333⋅8.3145⋅36550⋅ln(101.2663)
Next Step Evaluate
∴WIsothermal=4814696.07493673J
Next Step Convert to Output's Unit
∴WIsothermal=4814.69607493673KJ
LAST Step Rounding Answer
∴WIsothermal=4814.6961KJ

Work done during Isothermal Compression given Temperature and Volume 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 Refrigerant in kg per minute
Mass of refrigerant in kg per minute is the amount of refrigerant in kilograms that flows through the compressor per minute of operation.
Symbol: m
Measurement: Mass Flow RateUnit: kg/min
Note: Value should be greater than 0.
Formulas to find Mass of Refrigerant in kg per minuteOpen Variable
Temperature of Refrigerant
Temperature of Refrigerant is the temperature of the refrigerant at the end of the compression process in a single stage compressor.
Symbol: T
Measurement: TemperatureUnit: K
Note: Value can be positive or negative.
Formulas to find Temperature of RefrigerantOpen Variable
Suction Volume
Suction volume is the volume of air drawn into the compressor's cylinder during the suction stroke of a single stage compression process.
Symbol: V1
Measurement: VolumeUnit: m³
Note: Value can be positive or negative.
Formulas to find Suction VolumeOpen Variable
Discharge Volume
Discharge Volume is the volume of gas displaced by the piston during a single stroke in a single stage compressor operation.
Symbol: V2
Measurement: VolumeUnit: m³
Note: Value can be positive or negative.
Formulas to find Discharge VolumeOpen 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 Compression Ratio
WIsothermal=2.3⋅mgas⋅[R]⋅T1⋅ln(r)
​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 Volume Ratio?

Work done during Isothermal Compression given Temperature and Volume Ratio evaluator uses 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) to evaluate the Work done per minute during Isothermal Compression, Work done during Isothermal Compression given Temperature and Volume Ratio formula is defined as the energy transferred during the compression process of a refrigerant in a closed system at a constant temperature, where the volume ratio of the initial and final states is known. Work done per minute during Isothermal Compression is denoted by WIsothermal symbol.

How to evaluate Work done during Isothermal Compression given Temperature and Volume Ratio using this online evaluator? To use this online evaluator for Work done during Isothermal Compression given Temperature and Volume Ratio, enter Mass of Refrigerant in kg per minute (m), Temperature of Refrigerant (T), Suction Volume (V1) & Discharge Volume (V2) and hit the calculate button.

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

What is the formula to find Work done during Isothermal Compression given Temperature and Volume Ratio?
The formula of Work done during Isothermal Compression given Temperature and Volume Ratio is expressed as 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). Here is an example- 4.821283 = 2.3*3.33333333333333*[R]*36550*ln(10/1.26625).
How to calculate Work done during Isothermal Compression given Temperature and Volume Ratio?
With Mass of Refrigerant in kg per minute (m), Temperature of Refrigerant (T), Suction Volume (V1) & Discharge Volume (V2) we can find Work done during Isothermal Compression given Temperature and Volume Ratio using the formula - 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). 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 Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)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 Volume Ratio be negative?
Yes, the Work done during Isothermal Compression given Temperature and Volume Ratio, measured in Energy can be negative.
Which unit is used to measure Work done during Isothermal Compression given Temperature and Volume Ratio?
Work done during Isothermal Compression given Temperature and Volume 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 Volume Ratio can be measured.
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