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Work done during isentropic compression Formula

GoWork done during isentropic Compression given Specific Heat Capacity Constant Pressure Formula

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Work done per minute during Isentropic Compression is the energy transferred per minute during the reversible adiabatic compression of a gas in a single stage compressor. Check FAQs

W Isentropic = (\frac{γ}{γ - 1}) \cdot m \cdot [R] \cdot (T discharge - T refrigerant)

W_Isentropic - Work done per minute during Isentropic Compression?γ - Isentropic Index?m - Mass of Refrigerant in kg per minute?T_discharge - Discharge Temperature of Refrigerant?T_refrigerant - Suction Temperature of Refrigerant?[R] - Universal gas constant?

Work done during isentropic compression Example

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Here is how the Work done during isentropic compression equation looks like with Values.

Here is how the Work done during isentropic compression equation looks like with Units.

Here is how the Work done during isentropic compression equation looks like.

582012.3833 = (\frac{1.4}{1.4 - 1}) \cdot 200 \cdot 8.3145 \cdot (450 - 350)

582012.3833J/min = (\frac{1.4}{1.4 - 1}) \cdot 200kg/min \cdot 8.3145 \cdot (450K - 350K)

582012.3833 = (\frac{1.4}{1.4 - 1}) \cdot 200 \cdot 8.3145 \cdot (450 - 350)

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Work done during isentropic compression Solution

Follow our step by step solution on how to calculate Work done during isentropic compression?

FIRST Step Consider the formula

W Isentropic = (\frac{γ}{γ - 1}) \cdot m \cdot [R] \cdot (T discharge - T refrigerant)

Next Step Substitute values of Variables

∴

W Isentropic = (\frac{1.4}{1.4 - 1}) \cdot 200kg/min \cdot [R] \cdot (450K - 350K)

Next Step Substitute values of Constants

∴

W Isentropic = (\frac{1.4}{1.4 - 1}) \cdot 200kg/min \cdot 8.3145 \cdot (450K - 350K)

Next Step Convert Units

∴

W Isentropic = (\frac{1.4}{1.4 - 1}) \cdot 3.3333kg/s \cdot 8.3145 \cdot (450K - 350K)

Next Step Prepare to Evaluate

∴

W Isentropic = (\frac{1.4}{1.4 - 1}) \cdot 3.3333 \cdot 8.3145 \cdot (450 - 350)

Next Step Evaluate

∴

W Isentropic = 9700.20638784544J/s

Next Step Convert to Output's Unit

∴

W Isentropic = 582012.383270726J/min

LAST Step Rounding Answer

∴

W Isentropic = 582012.3833J/min

Work done during isentropic compression Formula Elements

Variables

Constants

Work done per minute during Isentropic Compression

Work done per minute during Isentropic Compression is the energy transferred per minute during the reversible adiabatic compression of a gas in a single stage compressor.

Symbol: W_Isentropic

Measurement: Rate of Heat TransferUnit: J/min

Note: Value can be positive or negative.

Formulas to find Work done per minute during Isentropic Compression

Isentropic Index

Isentropic Index is a measure of the efficiency of a compressor, describing the ratio of the compressor's actual performance to its ideal performance.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Isentropic Index

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 minute

Discharge Temperature of Refrigerant

Discharge Temperature of Refrigerant is the temperature of refrigerant at the outlet of a single stage compressor after compression is complete.

Symbol: T_discharge

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Discharge Temperature of Refrigerant

Suction Temperature of Refrigerant

Suction Temperature of Refrigerant is the temperature of the refrigerant at the suction port of a single stage compressor during the compression process.

Symbol: T_refrigerant

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Suction Temperature of Refrigerant

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

Other Formulas to find Work done per minute during Isentropic Compression

Go Work done during isentropic Compression given Specific Heat Capacity Constant Pressure

W Isentropic = m \cdot C p \cdot (T discharge - T refrigerant)

Other formulas in Work Done by Single Stage Compressor category

Go Work done during Isothermal Compression given Temperature and Compression Ratio

W Isothermal = 2.3 \cdot m gas \cdot [R] \cdot T 1 \cdot \ln (r)

Go Work done during Isothermal Compression given Temperature and Volume Ratio

W Isothermal = 2.3 \cdot m \cdot [R] \cdot T \cdot \ln (\frac{V 1}{V 2})

Go Work done during Isothermal Compression given Temperature and Pressure Ratio

W Isothermal = 2.3 \cdot m \cdot [R] \cdot T \cdot \ln (\frac{P 2}{P 1})

Go Work done during Isothermal Compression given Pressure and Volume Ratio

W Isothermal = 2.3 \cdot P 1 \cdot V 1 \cdot \ln (\frac{V 1}{V 2})

How to Evaluate Work done during isentropic compression?

Work done during isentropic compression evaluator uses Work done per minute during Isentropic Compression = (Isentropic Index/(Isentropic Index-1))*Mass of Refrigerant in kg per minute*[R]*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant) to evaluate the Work done per minute during Isentropic Compression, Work done during isentropic compression formula is defined as the energy transferred during the reversible adiabatic compression of a gas, typically in a compressor, where the temperature and pressure of the gas change without any heat transfer or change in entropy. Work done per minute during Isentropic Compression is denoted by W_Isentropic symbol.

How to evaluate Work done during isentropic compression using this online evaluator? To use this online evaluator for Work done during isentropic compression, enter Isentropic Index (γ), Mass of Refrigerant in kg per minute (m), Discharge Temperature of Refrigerant (T_discharge) & Suction Temperature of Refrigerant (T_refrigerant) and hit the calculate button.

FAQs on Work done during isentropic compression

What is the formula to find Work done during isentropic compression?

The formula of Work done during isentropic compression is expressed as Work done per minute during Isentropic Compression = (Isentropic Index/(Isentropic Index-1))*Mass of Refrigerant in kg per minute*[R]*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant). Here is an example- 3.5E+7 = (1.4/(1.4-1))*3.33333333333333*[R]*(450-350).

How to calculate Work done during isentropic compression?

With Isentropic Index (γ), Mass of Refrigerant in kg per minute (m), Discharge Temperature of Refrigerant (T_discharge) & Suction Temperature of Refrigerant (T_refrigerant) we can find Work done during isentropic compression using the formula - Work done per minute during Isentropic Compression = (Isentropic Index/(Isentropic Index-1))*Mass of Refrigerant in kg per minute*[R]*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant). This formula also uses Universal gas constant .

What are the other ways to Calculate Work done per minute during Isentropic Compression?

Here are the different ways to Calculate Work done per minute during Isentropic Compression-

Work done per minute during Isentropic Compression=Mass of Refrigerant in kg per minute*Specific Heat Capacity at Constant Pressure*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant)

Can the Work done during isentropic compression be negative?

Yes, the Work done during isentropic compression, measured in Rate of Heat Transfer can be negative.

Which unit is used to measure Work done during isentropic compression?

Work done during isentropic compression is usually measured using the Joule per Minute[J/min] for Rate of Heat Transfer. Joule per Second[J/min], Megajoule per Second[J/min], Kilojoule per Second[J/min] are the few other units in which Work done during isentropic compression can be measured.

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Work done during isentropic compression Formula

​GoWork done during isentropic Compression given Specific Heat Capacity Constant Pressure Formula

Work done during isentropic compression Example

Work done during isentropic compression Solution

Work done during isentropic compression Formula Elements

Other Formulas to find Work done per minute during Isentropic Compression

Other formulas in Work Done by Single Stage Compressor category

How to Evaluate Work done during isentropic compression?

FAQs on Work done during isentropic compression

Variable Name

GoWork done during isentropic Compression given Specific Heat Capacity Constant Pressure Formula