Work done during Isothermal Compression given Temperature and Pressure 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%
✖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%
✖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%

✖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 Pressure Ratio [W_Isothermal]

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Work done during Isothermal Compression given Temperature and Pressure 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(Discharge Pressure of Refrigerant/Suction Pressure)
W_Isothermal = 2.3*m*[R]*T*ln(P₂/P₁)
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.
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.
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.

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
Discharge Pressure of Refrigerant: 8 Bar --> 800000 Pascal (Check conversion here)
Suction Pressure: 1.013 Bar --> 101300 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_Isothermal = 2.3*m*[R]*T*ln(P₂/P₁) --> 2.3*3.33333333333333*[R]*36550*ln(800000/101300)

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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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 Temperature and Pressure Ratio Formula

LaTeX Go

What is Isothermal Compression Efficiency?

A measure of the performance of a reciprocating air compressor. It is expressed as a ratio of the isothermal work input to the actual work input. Isothermal compression is an ideal case since none of the work input is absorbed in raising the temperature of the compressed air, i.e. in raising its internal energy.

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

Work done during Isothermal Compression given Temperature and Pressure Ratio calculator uses 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) to calculate the Work done per minute during Isothermal Compression, Work done during Isothermal Compression given Temperature and Pressure Ratio formula is defined as the energy transferred during the compression process of a refrigerant in a single-stage compressor, where the temperature remains constant, and the pressure ratio is the key factor in determining the work done. Work done per minute during Isothermal Compression is denoted by W_Isothermal symbol.

How to calculate Work done during Isothermal Compression given Temperature and Pressure Ratio using this online calculator? To use this online calculator for Work done during Isothermal Compression given Temperature and Pressure Ratio, enter Mass of Refrigerant in kg per minute (m), Temperature of Refrigerant (T), Discharge Pressure of Refrigerant (P₂) & Suction Pressure (P₁) and hit the calculate button. Here is how the Work done during Isothermal Compression given Temperature and Pressure Ratio calculation can be explained with given input values -> 4.821283 = 2.3*3.33333333333333*[R]*36550*ln(800000/101300).

FAQ

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

Work done during Isothermal Compression given Temperature and Pressure Ratio formula is defined as the energy transferred during the compression process of a refrigerant in a single-stage compressor, where the temperature remains constant, and the pressure ratio is the key factor in determining the work done and is represented as W_Isothermal = 2.3*m*[R]*T*ln(P₂/P₁) or 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). 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, Discharge Pressure of Refrigerant is the pressure of refrigerant at the outlet of a single stage compressor after work is done on it & Suction pressure is the pressure of the fluid at the inlet of a compressor, which affects the compressor's performance and work done.

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

Work done during Isothermal Compression given Temperature and Pressure Ratio formula is defined as the energy transferred during the compression process of a refrigerant in a single-stage compressor, where the temperature remains constant, and the pressure ratio is the key factor in determining the work done is calculated using 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). To calculate Work done during Isothermal Compression given Temperature and Pressure Ratio, you need Mass of Refrigerant in kg per minute (m), Temperature of Refrigerant (T), Discharge Pressure of Refrigerant (P₂) & Suction Pressure (P₁). With our tool, you need to enter the respective value for Mass of Refrigerant in kg per minute, Temperature of Refrigerant, Discharge Pressure of Refrigerant & Suction Pressure 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, Discharge Pressure of Refrigerant & Suction Pressure. 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*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume)

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