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)
WIsothermal = 2.3*mgas*[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 per minute is the work done on the system during the isothermal compression of refrigerant.
Mass of Gas - (Measured in Kilogram) - Mass of Gas is the mass on or by which the work is done.
Temperature of Gas 1 - (Measured in Kelvin) - The Temperature of Gas 1 is the measure of the hotness or coldness of a gas.
Compression Ratio - Compression ratio is the ratio of the absolute stage discharge pressure to the absolute stage suction pressure.
STEP 1: Convert Input(s) to Base Unit
Mass of Gas: 11 Gram --> 0.011 Kilogram (Check conversion here)
Temperature of Gas 1: 200 Kelvin --> 200 Kelvin No Conversion Required
Compression Ratio: 4.75 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
WIsothermal = 2.3*mgas*[R]*T1*ln(r) --> 2.3*0.011*[R]*200*ln(4.75)
Evaluating ... ...
WIsothermal = 65.552984012949
STEP 3: Convert Result to Output's Unit
65.552984012949 Joule -->0.065552984012949 Kilojoule (Check conversion here)
FINAL ANSWER
0.065552984012949 0.065553 Kilojoule <-- Work done per minute during Isothermal Compression
(Calculation completed in 00.004 seconds)

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8 Work done by Single-Stage, Single Acting Reciprocating Compressor without Clearance Volume Calculators

Work done during polytropic compression
Go Work done per minute during Polytropic Compression = (Polytropic Index/(Polytropic Index-1))*Mass of refrigerant in kg per minute*[R]*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant)
Work done during isentropic compression
Go Work done per minute during Isentropic Compression = (Isentropic Index/(Isentropic Index-1))*Mass of refrigerant in kg per minute*[R]*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant)
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]*Suction 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]*Suction Temperature of Refrigerant*ln(Suction volume/Discharge Volume)
Work done during isentropic Compression given Specific Heat Capacity Constant Pressure
Go Work done per minute during Isentropic Compression = Mass of refrigerant in kg per minute*Specific Heat Capacity at Constant Pressure*(Discharge Temperature of Refrigerant-Suction Temperature of Refrigerant)
Work done during Isothermal Compression given Volume and Pressure Ratio
Go Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure)
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 Temperature and Compression Ratio Formula

Work done per minute during Isothermal Compression = 2.3*Mass of Gas*[R]*Temperature of Gas 1*ln(Compression Ratio)
WIsothermal = 2.3*mgas*[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, The Work done during Isothermal Compression given Temperature and Compression Ratio calculates the work done on the system during the isothermal compression of refrigerant. Work done per minute during Isothermal Compression is denoted by WIsothermal 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 (mgas), 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 -> 6.6E-5 = 2.3*0.011*[R]*200*ln(4.75).

FAQ

What is Work done during Isothermal Compression given Temperature and Compression Ratio?
The Work done during Isothermal Compression given Temperature and Compression Ratio calculates the work done on the system during the isothermal compression of refrigerant and is represented as WIsothermal = 2.3*mgas*[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 mass on or by which the work is done, The Temperature of Gas 1 is the measure of the hotness or coldness of a gas & Compression ratio is the ratio of the absolute stage discharge pressure to the absolute stage suction pressure.
How to calculate Work done during Isothermal Compression given Temperature and Compression Ratio?
The Work done during Isothermal Compression given Temperature and Compression Ratio calculates the work done on the system during the isothermal compression of refrigerant 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 (mgas), 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 4 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]*Suction 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]*Suction 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)
  • Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure)
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