Work done during Isothermal Compression given Temperature and Compression Ratio Calculator

✖Mass of Gas is the quantity of gas processed by a single stage compressor, typically measured in units of mass per unit time.ⓘ Mass of Gas [m_gas]			+10% -10%
✖Temperature of Gas 1 is the temperature of the gas at the inlet of the compressor in a single stage compression process.ⓘ Temperature of Gas 1 [T₁]			+10% -10%
✖Compression Ratio is the ratio of the volume of air or gas in a compressor at inlet to the volume at outlet in a single stage compression process.ⓘ Compression Ratio [r]			+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 Compression Ratio [W_Isothermal]

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Work done during Isothermal Compression given Temperature and Compression Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)
W_Isothermal = 2.3*m_gas*[R]*T₁*ln(r)
This formula uses 1 Constants, 1 Functions, 4 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 Gas - (Measured in Kilogram) - Mass of Gas is the quantity of gas processed by a single stage compressor, typically measured in units of mass per unit time.
Temperature of Gas 1 - (Measured in Kelvin) - Temperature of Gas 1 is the temperature of the gas at the inlet of the compressor in a single stage compression process.
Compression Ratio - Compression Ratio is the ratio of the volume of air or gas in a compressor at inlet to the volume at outlet in a single stage compression process.

STEP 1: Convert Input(s) to Base Unit

Mass of Gas: 716470 Gram --> 716.47 Kilogram (Check conversion here)
Temperature of Gas 1: 225.5 Kelvin --> 225.5 Kelvin No Conversion Required
Compression Ratio: 4.75 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_Isothermal = 2.3*m_gas*[R]*T₁*ln(r) --> 2.3*716.47*[R]*225.5*ln(4.75)

Evaluating ... ...

W_Isothermal = 4814091.51171515

STEP 3: Convert Result to Output's Unit

4814091.51171515 Joule -->4814.09151171515 Kilojoule (Check conversion here)

FINAL ANSWER

4814.09151171515 ≈ 4814.092 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 Compression 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 Temperature and Compression Ratio Formula

LaTeX Go

Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)
W_Isothermal = 2.3*m_gas*[R]*T₁*ln(r)

What is Work Done in Compression?

Gases can do work through expansion or compression against constant external pressure. Work done by gases is also sometimes called pressure-volume or PV work for reasons that will hopefully become more clear in this section.

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

Work done during Isothermal Compression given Temperature and Compression Ratio calculator uses Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio) to calculate the Work done per minute during Isothermal Compression, Work done during Isothermal Compression given Temperature and Compression Ratio formula is defined as the energy transferred to the system during the compression process, where the temperature remains constant, and is a critical parameter in evaluating 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 Temperature and Compression Ratio using this online calculator? To use this online calculator for Work done during Isothermal Compression given Temperature and Compression Ratio, enter Mass of Gas (m_gas), Temperature of Gas 1 (T₁) & Compression Ratio (r) and hit the calculate button. Here is how the Work done during Isothermal Compression given Temperature and Compression Ratio calculation can be explained with given input values -> 4.269704 = 2.3*716.47*[R]*225.5*ln(4.75).

FAQ

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

Work done during Isothermal Compression given Temperature and Compression Ratio formula is defined as the energy transferred to the system during the compression process, where the temperature remains constant, and is a critical parameter in evaluating the performance of a single-stage compressor and is represented as W_Isothermal = 2.3*m_gas*[R]*T₁*ln(r) or Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio). Mass of Gas is the quantity of gas processed by a single stage compressor, typically measured in units of mass per unit time, Temperature of Gas 1 is the temperature of the gas at the inlet of the compressor in a single stage compression process & Compression Ratio is the ratio of the volume of air or gas in a compressor at inlet to the volume at outlet in a single stage compression process.

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

Work done during Isothermal Compression given Temperature and Compression Ratio formula is defined as the energy transferred to the system during the compression process, where the temperature remains constant, and is a critical parameter in evaluating the performance of a single-stage compressor is calculated using Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio). To calculate Work done during Isothermal Compression given Temperature and Compression Ratio, you need Mass of Gas (m_gas), Temperature of Gas 1 (T₁) & Compression Ratio (r). With our tool, you need to enter the respective value for Mass of Gas, Temperature of Gas 1 & Compression Ratio 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 Gas, Temperature of Gas 1 & Compression Ratio. 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 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)
Work done per minute during Isothermal Compression = 2.3*Suction Pressure*Suction Volume*ln(Suction Volume/Discharge Volume)

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