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]*Suction Temperature of Refrigerant*ln(Suction volume/Discharge Volume)
WIsothermal = 2.3*m*[R]*Trefrigerant*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 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.
Suction volume - (Measured in Cubic Meter) - Suction volume is the volume of refrigerant sucked by the compressor during its suction stroke.
Discharge Volume - (Measured in Cubic Meter) - Discharge volume is the volume of the refrigerant after compression or at the discharge.
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
Suction volume: 10 Cubic Meter --> 10 Cubic Meter No Conversion Required
Discharge Volume: 1.6 Cubic Meter --> 1.6 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
WIsothermal = 2.3*m*[R]*Trefrigerant*ln(V1/V2) --> 2.3*0.0333333333333333*[R]*350*ln(10/1.6)
Evaluating ... ...
WIsothermal = 408.857623680665
STEP 3: Convert Result to Output's Unit
408.857623680665 Joule -->0.408857623680665 Kilojoule (Check conversion here)
FINAL ANSWER
0.408857623680665 0.408858 Kilojoule <-- Work done per minute during Isothermal Compression
(Calculation completed in 00.020 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 Volume Ratio Formula

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)
WIsothermal = 2.3*m*[R]*Trefrigerant*ln(V1/V2)

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]*Suction Temperature of Refrigerant*ln(Suction volume/Discharge Volume) to calculate the Work done per minute during Isothermal Compression, The Work done during Isothermal Compression given Temperature and Volume Ratio calculates the work done on the system during the isothermal compression of refrigerant when the suction temperature, suction, and discharge volume 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 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), Suction Temperature of Refrigerant (Trefrigerant), 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 -> 0.000409 = 2.3*0.0333333333333333*[R]*350*ln(10/1.6).

FAQ

What is Work done during Isothermal Compression given Temperature and Volume Ratio?
The Work done during Isothermal Compression given Temperature and Volume Ratio calculates the work done on the system during the isothermal compression of refrigerant when the suction temperature, suction, and discharge volume is given and is represented as WIsothermal = 2.3*m*[R]*Trefrigerant*ln(V1/V2) or 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). 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, Suction volume is the volume of refrigerant sucked by the compressor during its suction stroke & Discharge volume is the volume of the refrigerant after compression or at the discharge.
How to calculate Work done during Isothermal Compression given Temperature and Volume Ratio?
The Work done during Isothermal Compression given Temperature and Volume Ratio calculates the work done on the system during the isothermal compression of refrigerant when the suction temperature, suction, and discharge volume 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(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), Suction Temperature of Refrigerant (Trefrigerant), Suction volume (V1) & Discharge Volume (V2). With our tool, you need to enter the respective value for Mass of refrigerant in kg per minute, Suction 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, Suction Temperature of Refrigerant, Suction volume & Discharge Volume. 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(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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