Work done during Isothermal Compression given Temperature and Volume Ratio Calculator

✖Mass of refrigerant in kg per minute is the amount of refrigerant in kilograms that flows through the compressor per minute of operation.ⓘ Mass of Refrigerant in kg per minute [m]			+10% -10%
✖Temperature of Refrigerant is the temperature of the refrigerant at the end of the compression process in a single stage compressor.ⓘ Temperature of Refrigerant [T]			+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 Temperature and Volume Ratio [W_Isothermal]

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Work done during Isothermal Compression given Temperature and Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
W_Isothermal = 2.3*m*[R]*T*ln(V₁/V₂)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

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.
Mass of Refrigerant in kg per minute - (Measured in Kilogram per Second) - Mass of refrigerant in kg per minute is the amount of refrigerant in kilograms that flows through the compressor per minute of operation.
Temperature of Refrigerant - (Measured in Kelvin) - Temperature of Refrigerant is the temperature of the refrigerant at the end of the compression process in a single stage compressor.
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

Mass of Refrigerant in kg per minute: 200 Kilogram per Minute --> 3.33333333333333 Kilogram per Second (Check conversion here)
Temperature of Refrigerant: 36550 Kelvin --> 36550 Kelvin No Conversion Required
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*m*[R]*T*ln(V₁/V₂) --> 2.3*3.33333333333333*[R]*36550*ln(10/1.26625)

Evaluating ... ...

W_Isothermal = 4814696.07493673

STEP 3: Convert Result to Output's Unit

4814696.07493673 Joule -->4814.69607493673 Kilojoule (Check conversion here)

FINAL ANSWER

4814.69607493673 ≈ 4814.696 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 Temperature 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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National Institute Of Technology (NIT), Hamirpur

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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 Temperature and Volume Ratio Formula

LaTeX Go

What is Isothermal Process?

An isothermal process is a thermodynamic process in which the temperature of a system remains constant. The transfer of heat into or out of the system happens so slowly that thermal equilibrium is maintained.

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

Work done during Isothermal Compression given Temperature and Volume Ratio calculator 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 calculate 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 W_Isothermal symbol.

How to calculate Work done during Isothermal Compression given Temperature and Volume Ratio using this online calculator? To use this online calculator 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. Here is how the Work done during Isothermal Compression given Temperature and Volume Ratio calculation can be explained with given input values -> 4.821283 = 2.3*3.33333333333333*[R]*36550*ln(10/1.26625).

FAQ

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

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 and is represented as W_Isothermal = 2.3*m*[R]*T*ln(V₁/V₂) or 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). Mass of refrigerant in kg per minute is the amount of refrigerant in kilograms that flows through the compressor per minute of operation, Temperature of Refrigerant is the temperature of the refrigerant at the end of the compression process in a single stage compressor, 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 Temperature and Volume Ratio?

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 is calculated using 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 calculate Work done during Isothermal Compression given Temperature and Volume Ratio, you need Mass of Refrigerant in kg per minute (m), Temperature of Refrigerant (T), Suction Volume (V₁) & Discharge Volume (V₂). With our tool, you need to enter the respective value for Mass of Refrigerant in kg per minute, Temperature of Refrigerant, 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 Mass of Refrigerant in kg per minute, Temperature of Refrigerant, 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(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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