Work done during Isothermal Compression given Volume and Pressure Ratio Calculator

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✖The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.ⓘ Suction pressure [P₁]			+10% -10%
✖Suction volume is the volume of refrigerant sucked by the compressor during its suction stroke.ⓘ Suction volume [V₁]			+10% -10%
✖The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.ⓘ Discharge Pressure of Refrigerant [P₂]			+10% -10%

✖Work done per minute during Isothermal Compression per minute is the work done on the system during the isothermal compression of refrigerant.ⓘ Work done during Isothermal Compression given Volume and Pressure Ratio [W_Isothermal]

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Work done during Isothermal Compression given Volume and Pressure Ratio

Formula

`"W"_{"Isothermal"} = 2.3*"P"_{"1"}*"V"_{"1"}*ln("P"_{"2"}/"P"_{"1"})`

Example

`"4814.797KJ"=2.3*"1.013Bar"*"10m³"*ln("8Bar"/"1.013Bar")`

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Work done during Isothermal Compression given Volume and Pressure Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure)
W_Isothermal = 2.3*P₁*V₁*ln(P₂/P₁)
This formula uses 1 Functions, 4 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Work done per minute during Isothermal Compression - (Measured in Joule) - Work done per minute during Isothermal Compression per minute is the work done on the system during the isothermal compression of refrigerant.
Suction pressure - (Measured in Pascal) - The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.
Suction volume - (Measured in Cubic Meter) - Suction volume is the volume of refrigerant sucked by the compressor during its suction stroke.
Discharge Pressure of Refrigerant - (Measured in Pascal) - The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.

STEP 1: Convert Input(s) to Base Unit

Suction pressure: 1.013 Bar --> 101300 Pascal (Check conversion here)
Suction volume: 10 Cubic Meter --> 10 Cubic Meter No Conversion Required
Discharge Pressure of Refrigerant: 8 Bar --> 800000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_Isothermal = 2.3*P₁*V₁*ln(P₂/P₁) --> 2.3*101300*10*ln(800000/101300)

Evaluating ... ...

W_Isothermal = 4814797.33471132

STEP 3: Convert Result to Output's Unit

4814797.33471132 Joule -->4814.79733471132 Kilojoule (Check conversion here)

FINAL ANSWER

4814.79733471132 ≈ 4814.797 Kilojoule <-- Work done per minute during Isothermal Compression

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Work Done by Single-Stage Compressor » Work done during Isothermal Compression given Volume and Pressure Ratio

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Created by Abhishek Dharmendra Bansile

Vishwakarma Institute of Information Technology, Pune (VIIT Pune), Pune

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< 8 Work Done by Single-Stage Compressor Calculators

Work done during polytropic compression

Go Work done per minute during Polytropic Compression = (Polytropic Index/(Polytropic Index-1))*Mass of refrigerant in kg per minute*[R]*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant)

Work done during isentropic compression

Go 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)

Work done during Isothermal Compression given Temperature and Pressure Ratio

Go Work done per minute during Isothermal Compression = 2.3*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction pressure)

Work done during Isothermal Compression given Temperature and Volume Ratio

Go Work done per minute during Isothermal Compression = 2.3*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*ln(Suction volume/Discharge Volume)

Work done during isentropic Compression given Specific Heat Capacity Constant Pressure

Go 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)

Work done during Isothermal Compression given Volume and Pressure Ratio

Go Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure)

Work done during Isothermal Compression given Pressure and Volume Ratio

Go Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Suction volume/Discharge Volume)

Work done during Isothermal Compression given Temperature and Compression Ratio

Go Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)

Work done during Isothermal Compression given Volume and Pressure Ratio Formula

Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure)
W_Isothermal = 2.3*P₁*V₁*ln(P₂/P₁)

What is an example of an isothermal process?

The thermodynamics process in which the temperature of the whole system remains constant over a period of time is called isothermal process. So, the constant temperature of any system makes the process an isothermal process. For example, melting of ice at zero degree is such an example of an isothermal process.

How to Calculate Work done during Isothermal Compression given Volume and Pressure Ratio?

Work done during Isothermal Compression given Volume and Pressure Ratio calculator uses Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure) to calculate the Work done per minute during Isothermal Compression, The Work done during Isothermal Compression given Volume and Pressure Ratio calculates the work done on the system during the isothermal compression of refrigerant. Work done per minute during Isothermal Compression is denoted by W_Isothermal symbol.

How to calculate Work done during Isothermal Compression given Volume and Pressure Ratio using this online calculator? To use this online calculator for Work done during Isothermal Compression given Volume and Pressure Ratio, enter Suction pressure (P₁), Suction volume (V₁) & Discharge Pressure of Refrigerant (P₂) and hit the calculate button. Here is how the Work done during Isothermal Compression given Volume and Pressure Ratio calculation can be explained with given input values -> 4.814797 = 2.3*101300*10*ln(800000/101300).

FAQ

What is Work done during Isothermal Compression given Volume and Pressure Ratio?

The Work done during Isothermal Compression given Volume and Pressure Ratio calculates the work done on the system during the isothermal compression of refrigerant and is represented as W_Isothermal = 2.3*P₁*V₁*ln(P₂/P₁) or Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure). The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant, Suction volume is the volume of refrigerant sucked by the compressor during its suction stroke & The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.

How to calculate Work done during Isothermal Compression given Volume and Pressure Ratio?

The Work done during Isothermal Compression given Volume and Pressure Ratio calculates the work done on the system during the isothermal compression of refrigerant is calculated using Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure). To calculate Work done during Isothermal Compression given Volume and Pressure Ratio, you need Suction pressure (P₁), Suction volume (V₁) & Discharge Pressure of Refrigerant (P₂). With our tool, you need to enter the respective value for Suction pressure, Suction volume & Discharge Pressure of Refrigerant 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 Work done per minute during Isothermal Compression?

In this formula, Work done per minute during Isothermal Compression uses Suction pressure, Suction volume & Discharge Pressure of Refrigerant. We can use 4 other way(s) to calculate the same, which is/are as follows -

Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)
Work done per minute during Isothermal Compression = 2.3*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*ln(Suction volume/Discharge Volume)
Work done per minute during Isothermal Compression = 2.3*Mass of refrigerant in kg per minute*[R]*Suction Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction pressure)
Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Suction volume/Discharge Volume)

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