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]*Suction Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction pressure)
WIsothermal = 2.3*m*[R]*Trefrigerant*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 per minute is the work done on the system during the isothermal compression of refrigerant.
Mass of refrigerant in kg per minute - (Measured in Kilogram per Second) - Mass of refrigerant in kg per minute is the mass on or by which the work is done.
Suction Temperature of Refrigerant - (Measured in Kelvin) - The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke.
Discharge Pressure of Refrigerant - (Measured in Pascal) - The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge.
Suction pressure - (Measured in Pascal) - The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.
STEP 1: Convert Input(s) to Base Unit
Mass of refrigerant in kg per minute: 2 Kilogram per Minute --> 0.0333333333333333 Kilogram per Second (Check conversion here)
Suction Temperature of Refrigerant: 350 Kelvin --> 350 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
WIsothermal = 2.3*m*[R]*Trefrigerant*ln(P2/P1) --> 2.3*0.0333333333333333*[R]*350*ln(800000/101300)
Evaluating ... ...
WIsothermal = 461.05160772308
STEP 3: Convert Result to Output's Unit
461.05160772308 Joule -->0.46105160772308 Kilojoule (Check conversion here)
FINAL ANSWER
0.46105160772308 0.461052 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 Pressure Ratio Formula

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)
WIsothermal = 2.3*m*[R]*Trefrigerant*ln(P2/P1)

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]*Suction Temperature of Refrigerant*ln(Discharge Pressure of Refrigerant/Suction pressure) to calculate the Work done per minute during Isothermal Compression, The Work done during Isothermal Compression given Temperature and Pressure Ratio calculates the work done on the system during the isothermal compression of refrigerant when the suction temperature, suction, and discharge pressure is given. Work done per minute during Isothermal Compression is denoted by WIsothermal 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), Suction Temperature of Refrigerant (Trefrigerant), 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 -> 0.000461 = 2.3*0.0333333333333333*[R]*350*ln(800000/101300).

FAQ

What is Work done during Isothermal Compression given Temperature and Pressure Ratio?
The Work done during Isothermal Compression given Temperature and Pressure Ratio calculates the work done on the system during the isothermal compression of refrigerant when the suction temperature, suction, and discharge pressure is given and is represented as WIsothermal = 2.3*m*[R]*Trefrigerant*ln(P2/P1) or 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). Mass of refrigerant in kg per minute is the mass on or by which the work is done, The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke, The discharge pressure of refrigerant is the pressure of the refrigerant after the compression stage or it is the pressure of the refrigerant at the discharge & The Suction Pressure is the pressure of the refrigerant before the compression. It is also called the suction pressure of the refrigerant.
How to calculate Work done during Isothermal Compression given Temperature and Pressure Ratio?
The Work done during Isothermal Compression given Temperature and Pressure Ratio calculates the work done on the system during the isothermal compression of refrigerant when the suction temperature, suction, and discharge pressure is given is calculated using 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). To calculate Work done during Isothermal Compression given Temperature and Pressure Ratio, you need Mass of refrigerant in kg per minute (m), Suction Temperature of Refrigerant (Trefrigerant), 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, Suction 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, Suction Temperature of Refrigerant, Discharge Pressure of Refrigerant & Suction pressure. 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 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]*Suction 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)
  • Work done per minute during Isothermal Compression = 2.3*Suction pressure*Suction volume*ln(Discharge Pressure of Refrigerant/Suction pressure)
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