Work done during Isothermal Compression given Volume and Pressure 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 Pressure of Refrigerant is the pressure of refrigerant at the outlet of a single stage compressor after work is done on it.ⓘ Discharge Pressure of Refrigerant [P₂]			+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 Volume and Pressure Ratio [W_Isothermal]

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Formula

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Work done during Isothermal Compression given Volume and Pressure Ratio

Formula

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

Example

4814.797 KJ = 2.3 \cdot 1.013 Bar \cdot 10 m³ \cdot \ln (\frac{8 Bar}{1.013 Bar})

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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 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 Pressure of Refrigerant - (Measured in Pascal) - Discharge Pressure of Refrigerant is the pressure of refrigerant at the outlet of a single stage compressor after work is done on it.

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 » Mechanical » 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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< Work Done by Single Stage Compressor Calculators

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]*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]*Temperature of Refrigerant*ln(Suction Volume/Discharge Volume)

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, Work done during Isothermal Compression given Volume and Pressure Ratio formula is defined as the energy transferred during the compression process in an isothermal system, where the temperature remains constant, and is a crucial parameter in understanding the performance of a single-stage compressor. 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?

Work done during Isothermal Compression given Volume and Pressure Ratio formula is defined as the energy transferred during the compression process in an isothermal system, where the temperature remains constant, and is a crucial parameter in understanding the performance of a single-stage compressor 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). 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 Pressure of Refrigerant is the pressure of refrigerant at the outlet of a single stage compressor after work is done on it.

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

Work done during Isothermal Compression given Volume and Pressure Ratio formula is defined as the energy transferred during the compression process in an isothermal system, where the temperature remains constant, and is a crucial parameter in understanding the performance of a single-stage compressor 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 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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