Total Work done per cycle in Compressor during Incomplete Intercooling given Volume Calculator

✖Polytropic Index for Compression is a measure of the efficiency of a two-stage compressor, indicating the degree of isentropic compression in a real compression process.ⓘ Polytropic Index for Compression [n_c]			+10% -10%
✖Suction Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor in a two-stage compressor system draws in air or gas.ⓘ Suction Pressure of Low Pressure Compressor [P₁]			+10% -10%
✖Suction Volume of High Pressure Compressor is the volume of air sucked by the high-pressure compressor in a two-stage compression system.ⓘ Suction Volume of High Pressure Compressor [V_1,hc]			+10% -10%
✖Discharge Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor stage of a two-stage compressor discharges compressed air or gas.ⓘ Discharge Pressure of Low Pressure Compressor [P₂]			+10% -10%
✖Discharge Volume of High Pressure Compressor is the volume of gas discharged by the high-pressure compressor in a two-stage compression system.ⓘ Discharge Volume of High Pressure Compressor [V_2,hc]			+10% -10%
✖Discharge Pressure of High Pressure Compressor is the pressure at which the high-pressure compressor stage of a two-stage compressor discharges compressed air or gas.ⓘ Discharge Pressure of High Pressure Compressor [P₃]			+10% -10%

✖Total Work Done per cycle is the total energy transferred per cycle in a two-stage compressor, which involves compression in two stages with intermediate cooling.ⓘ Total Work done per cycle in Compressor during Incomplete Intercooling given Volume [w_t]

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Formula

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Total Work done per cycle in Compressor during Incomplete Intercooling given Volume

Formula

w t = (\frac{n c}{n c - 1}) \cdot P 1 \cdot V 1,hc \cdot ({(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}} - 1) + (\frac{n c}{n c - 1}) \cdot P 2 \cdot V 2,hc \cdot ({(\frac{P 3}{P 2})}^{\frac{n c - 1}{n c}} - 1)

Example

341321.1 J = (\frac{1.2}{1.2 - 1}) \cdot 0.002 Bar \cdot 0.001 m³ \cdot ({(\frac{7 Bar}{0.002 Bar})}^{\frac{1.2 - 1}{1.2}} - 1) + (\frac{1.2}{1.2 - 1}) \cdot 7 Bar \cdot 0.6 m³ \cdot ({(\frac{15 Bar}{7 Bar})}^{\frac{1.2 - 1}{1.2}} - 1)

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Total Work done per cycle in Compressor during Incomplete Intercooling given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)
w_t = (n_c/(n_c-1))*P₁*V_1,hc*((P₂/P₁)^((n_c-1)/n_c)-1)+(n_c/(n_c-1))*P₂*V_2,hc*((P₃/P₂)^((n_c-1)/n_c)-1)
This formula uses 7 Variables

Variables Used

Total Work Done per Cycle - (Measured in Joule) - Total Work Done per cycle is the total energy transferred per cycle in a two-stage compressor, which involves compression in two stages with intermediate cooling.
Polytropic Index for Compression - Polytropic Index for Compression is a measure of the efficiency of a two-stage compressor, indicating the degree of isentropic compression in a real compression process.
Suction Pressure of Low Pressure Compressor - (Measured in Pascal) - Suction Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor in a two-stage compressor system draws in air or gas.
Suction Volume of High Pressure Compressor - (Measured in Cubic Meter) - Suction Volume of High Pressure Compressor is the volume of air sucked by the high-pressure compressor in a two-stage compression system.
Discharge Pressure of Low Pressure Compressor - (Measured in Pascal) - Discharge Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor stage of a two-stage compressor discharges compressed air or gas.
Discharge Volume of High Pressure Compressor - (Measured in Cubic Meter) - Discharge Volume of High Pressure Compressor is the volume of gas discharged by the high-pressure compressor in a two-stage compression system.
Discharge Pressure of High Pressure Compressor - (Measured in Pascal) - Discharge Pressure of High Pressure Compressor is the pressure at which the high-pressure compressor stage of a two-stage compressor discharges compressed air or gas.

STEP 1: Convert Input(s) to Base Unit

Polytropic Index for Compression: 1.2 --> No Conversion Required
Suction Pressure of Low Pressure Compressor: 0.002 Bar --> 200 Pascal (Check conversion here)
Suction Volume of High Pressure Compressor: 0.001 Cubic Meter --> 0.001 Cubic Meter No Conversion Required
Discharge Pressure of Low Pressure Compressor: 7 Bar --> 700000 Pascal (Check conversion here)
Discharge Volume of High Pressure Compressor: 0.6 Cubic Meter --> 0.6 Cubic Meter No Conversion Required
Discharge Pressure of High Pressure Compressor: 15 Bar --> 1500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w_t = (n_c/(n_c-1))*P₁*V_1,hc*((P₂/P₁)^((n_c-1)/n_c)-1)+(n_c/(n_c-1))*P₂*V_2,hc*((P₃/P₂)^((n_c-1)/n_c)-1) --> (1.2/(1.2-1))*200*0.001*((700000/200)^((1.2-1)/1.2)-1)+(1.2/(1.2-1))*700000*0.6*((1500000/700000)^((1.2-1)/1.2)-1)

Evaluating ... ...

w_t = 341321.148765162

STEP 3: Convert Result to Output's Unit

341321.148765162 Joule --> No Conversion Required

FINAL ANSWER

341321.148765162 ≈ 341321.1 Joule <-- Total Work Done per Cycle

(Calculation completed in 00.004 seconds)

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Home » Physics » Refrigeration and Air Conditioning » Refrigerant Compressors » Mechanical » Work Done by Two Stage Compressor » Total Work done per cycle in Compressor during Incomplete Intercooling given Volume

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Vishwakarma Institute of Information Technology, Pune (VIIT Pune), Pune

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< Work Done by Two Stage Compressor Calculators

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume

Go Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Total Work done per cycle in Compressor during incomplete Intercooling given Temperature

Go Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of Refrigerant in kg per minute*[R]*((Suction Temperature at Low Pressure Compressor*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))+Temperature at Exit of Intercooler*(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-Suction Temperature at Low Pressure Compressor-Temperature at Exit of Intercooler)

Work done per cycle in Low Pressure Compressor during incomplete intercooling given Suction Temp

Go Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of Refrigerant in kg per minute*[R]*Suction Temperature at Low Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Work done per cycle in Low pressure Compressor during incomplete intercooling given suction volume

Go Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume Formula

How does a Two stage reciprocating compressor work?

This type of compressor has two pistons which use for air compression. The piston of the L.P cylinder compresses the air and transfers the pressurized air into the second H.P for further compression where the second piston compresses it. These compressors operate with natural gas or electricity.

How to Calculate Total Work done per cycle in Compressor during Incomplete Intercooling given Volume?

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume calculator uses Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1) to calculate the Total Work Done per Cycle, Total Work done per cycle in Compressor during Incomplete Intercooling given Volume formula is defined as the energy transferred per cycle in a two-stage compressor with incomplete intercooling, which is a critical parameter in evaluating the performance of a compressor system. Total Work Done per Cycle is denoted by w_t symbol.

How to calculate Total Work done per cycle in Compressor during Incomplete Intercooling given Volume using this online calculator? To use this online calculator for Total Work done per cycle in Compressor during Incomplete Intercooling given Volume, enter Polytropic Index for Compression (n_c), Suction Pressure of Low Pressure Compressor (P₁), Suction Volume of High Pressure Compressor (V_1,hc), Discharge Pressure of Low Pressure Compressor (P₂), Discharge Volume of High Pressure Compressor (V_2,hc) & Discharge Pressure of High Pressure Compressor (P₃) and hit the calculate button. Here is how the Total Work done per cycle in Compressor during Incomplete Intercooling given Volume calculation can be explained with given input values -> 341352.4 = (1.2/(1.2-1))*200*0.001*((700000/200)^((1.2-1)/1.2)-1)+(1.2/(1.2-1))*700000*0.6*((1500000/700000)^((1.2-1)/1.2)-1).

FAQ

What is Total Work done per cycle in Compressor during Incomplete Intercooling given Volume?

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume formula is defined as the energy transferred per cycle in a two-stage compressor with incomplete intercooling, which is a critical parameter in evaluating the performance of a compressor system and is represented as w_t = (n_c/(n_c-1))*P₁*V_1,hc*((P₂/P₁)^((n_c-1)/n_c)-1)+(n_c/(n_c-1))*P₂*V_2,hc*((P₃/P₂)^((n_c-1)/n_c)-1) or Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1). Polytropic Index for Compression is a measure of the efficiency of a two-stage compressor, indicating the degree of isentropic compression in a real compression process, Suction Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor in a two-stage compressor system draws in air or gas, Suction Volume of High Pressure Compressor is the volume of air sucked by the high-pressure compressor in a two-stage compression system, Discharge Pressure of Low Pressure Compressor is the pressure at which the low-pressure compressor stage of a two-stage compressor discharges compressed air or gas, Discharge Volume of High Pressure Compressor is the volume of gas discharged by the high-pressure compressor in a two-stage compression system & Discharge Pressure of High Pressure Compressor is the pressure at which the high-pressure compressor stage of a two-stage compressor discharges compressed air or gas.

How to calculate Total Work done per cycle in Compressor during Incomplete Intercooling given Volume?

Total Work done per cycle in Compressor during Incomplete Intercooling given Volume formula is defined as the energy transferred per cycle in a two-stage compressor with incomplete intercooling, which is a critical parameter in evaluating the performance of a compressor system is calculated using Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume of High Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1)+(Polytropic Index for Compression/(Polytropic Index for Compression-1))*Discharge Pressure of Low Pressure Compressor*Discharge Volume of High Pressure Compressor*((Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-1). To calculate Total Work done per cycle in Compressor during Incomplete Intercooling given Volume, you need Polytropic Index for Compression (n_c), Suction Pressure of Low Pressure Compressor (P₁), Suction Volume of High Pressure Compressor (V_1,hc), Discharge Pressure of Low Pressure Compressor (P₂), Discharge Volume of High Pressure Compressor (V_2,hc) & Discharge Pressure of High Pressure Compressor (P₃). With our tool, you need to enter the respective value for Polytropic Index for Compression, Suction Pressure of Low Pressure Compressor, Suction Volume of High Pressure Compressor, Discharge Pressure of Low Pressure Compressor, Discharge Volume of High Pressure Compressor & Discharge Pressure of High Pressure Compressor 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 Total Work Done per Cycle?

In this formula, Total Work Done per Cycle uses Polytropic Index for Compression, Suction Pressure of Low Pressure Compressor, Suction Volume of High Pressure Compressor, Discharge Pressure of Low Pressure Compressor, Discharge Volume of High Pressure Compressor & Discharge Pressure of High Pressure Compressor. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of Refrigerant in kg per minute*[R]*((Suction Temperature at Low Pressure Compressor*(Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression))+Temperature at Exit of Intercooler*(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-Suction Temperature at Low Pressure Compressor-Temperature at Exit of Intercooler)
Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Mass of Refrigerant in kg per minute*[R]*Suction Temperature at Low Pressure Compressor*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)
Total Work Done per Cycle = (Polytropic Index for Compression/(Polytropic Index for Compression-1))*Suction Pressure of Low Pressure Compressor*Suction Volume*((Discharge Pressure of Low Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)+(Discharge Pressure of High Pressure Compressor/Discharge Pressure of Low Pressure Compressor)^((Polytropic Index for Compression-1)/Polytropic Index for Compression)-2)

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