Work done during Isothermal Compression given Pressure and Volume Ratio Calculator

✖Suction pressure is the pressure of the fluid at the inlet of a compressor, which affects the compressor's performance and work done.ⓘ Suction Pressure [P₁]			+10% -10%
✖Suction volume is the volume of air drawn into the compressor's cylinder during the suction stroke of a single stage compression process.ⓘ Suction Volume [V₁]			+10% -10%
✖Discharge Volume is the volume of gas displaced by the piston during a single stroke in a single stage compressor operation.ⓘ Discharge Volume [V₂]			+10% -10%

✖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.ⓘ Work done during Isothermal Compression given Pressure and Volume Ratio [W_Isothermal]

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Work done during Isothermal Compression given Pressure and Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume)
W_Isothermal = 2.3*P₁*V₁*ln(V₁/V₂)
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 is the energy transferred per minute during the isothermal compression of a gas in a single stage compressor.
Suction Pressure - (Measured in Pascal) - Suction pressure is the pressure of the fluid at the inlet of a compressor, which affects the compressor's performance and work done.
Suction Volume - (Measured in Cubic Meter) - Suction volume is the volume of air drawn into the compressor's cylinder during the suction stroke of a single stage compression process.
Discharge Volume - (Measured in Cubic Meter) - Discharge Volume is the volume of gas displaced by the piston during a single stroke in a single stage compressor operation.

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 Volume: 1.26625 Cubic Meter --> 1.26625 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_Isothermal = 2.3*P₁*V₁*ln(V₁/V₂) --> 2.3*101300*10*ln(10/1.26625)

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 » Mechanical » Work Done by Single Stage Compressor » Work done during Isothermal Compression given Pressure and Volume Ratio

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Created by Abhishek Dharmendra Bansile

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

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< Work Done by Single Stage Compressor Calculators

Work done during Isothermal Compression given Temperature and Pressure Ratio

LaTeX Go 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)

Work done during Isothermal Compression given Temperature and Volume Ratio

LaTeX Go 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)

Work done during Isothermal Compression given Pressure and Volume Ratio

LaTeX 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

LaTeX 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 Pressure and Volume Ratio Formula

LaTeX Go

Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume)
W_Isothermal = 2.3*P₁*V₁*ln(V₁/V₂)

Why is Isothermal Compression Positive?

The isothermal compression of the gas was performed in two ways, one irreversible and one reversible. The work done on the gas is positive because the gas is compressed; the surroundings do positive work on the gas. So the heat added to the compressed gas is negative, keeping the temperature constant.

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

Work done during Isothermal Compression given Pressure and Volume Ratio calculator uses Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume) to calculate the Work done per minute during Isothermal Compression, Work done during Isothermal Compression given Pressure and Volume Ratio formula is defined as the energy transferred during the compression process of an ideal gas at a constant temperature, where the pressure and volume ratio of the gas are known, and is a crucial parameter in understanding the thermodynamic behavior of the system. Work done per minute during Isothermal Compression is denoted by W_Isothermal symbol.

How to calculate Work done during Isothermal Compression given Pressure and Volume Ratio using this online calculator? To use this online calculator for Work done during Isothermal Compression given Pressure and Volume Ratio, enter Suction Pressure (P₁), Suction Volume (V₁) & Discharge Volume (V₂) and hit the calculate button. Here is how the Work done during Isothermal Compression given Pressure and Volume Ratio calculation can be explained with given input values -> 4.269732 = 2.3*101300*10*ln(10/1.26625).

FAQ

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

Work done during Isothermal Compression given Pressure and Volume Ratio formula is defined as the energy transferred during the compression process of an ideal gas at a constant temperature, where the pressure and volume ratio of the gas are known, and is a crucial parameter in understanding the thermodynamic behavior of the system and is represented as W_Isothermal = 2.3*P₁*V₁*ln(V₁/V₂) or Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume). Suction pressure is the pressure of the fluid at the inlet of a compressor, which affects the compressor's performance and work done, Suction volume is the volume of air drawn into the compressor's cylinder during the suction stroke of a single stage compression process & Discharge Volume is the volume of gas displaced by the piston during a single stroke in a single stage compressor operation.

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

Work done during Isothermal Compression given Pressure and Volume Ratio formula is defined as the energy transferred during the compression process of an ideal gas at a constant temperature, where the pressure and volume ratio of the gas are known, and is a crucial parameter in understanding the thermodynamic behavior of the system is calculated using Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume). To calculate Work done during Isothermal Compression given Pressure and Volume Ratio, you need Suction Pressure (P₁), Suction Volume (V₁) & Discharge Volume (V₂). With our tool, you need to enter the respective value for Suction Pressure, Suction Volume & Discharge Volume 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 Volume. We can use 3 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]*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]*Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction Pressure)

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