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Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Formula

GoTotal Work done per cycle in Compressor during incomplete Intercooling given Temperature Formula

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

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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. Check FAQs

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

w_t - Total Work Done per Cycle?n_c - Polytropic Index for Compression?P₁ - Suction Pressure of Low Pressure Compressor?V₁ - Suction Volume?P₂ - Discharge Pressure of Low Pressure Compressor?P₃ - Discharge Pressure of High Pressure Compressor?

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Example

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Here is how the Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature equation looks like with Values.

Here is how the Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature equation looks like with Units.

Here is how the Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature equation looks like.

36383.6804 = (\frac{1.2}{1.2 - 1}) \cdot 0.002 \cdot 10 \cdot ({(\frac{7}{0.002})}^{\frac{1.2 - 1}{1.2}} + {(\frac{15}{7})}^{\frac{1.2 - 1}{1.2}} - 2)

36383.6804J = (\frac{1.2}{1.2 - 1}) \cdot 0.002Bar \cdot 10m³ \cdot ({(\frac{7Bar}{0.002Bar})}^{\frac{1.2 - 1}{1.2}} + {(\frac{15Bar}{7Bar})}^{\frac{1.2 - 1}{1.2}} - 2)

36383.6804 = (\frac{1.2}{1.2 - 1}) \cdot 0.002 \cdot 10 \cdot ({(\frac{7}{0.002})}^{\frac{1.2 - 1}{1.2}} + {(\frac{15}{7})}^{\frac{1.2 - 1}{1.2}} - 2)

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Home » Physics » Mechanical » Refrigeration and Air Conditioning » Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Solution

Follow our step by step solution on how to calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 0.002Bar \cdot 10m³ \cdot ({(\frac{7Bar}{0.002Bar})}^{\frac{1.2 - 1}{1.2}} + {(\frac{15Bar}{7Bar})}^{\frac{1.2 - 1}{1.2}} - 2)

Next Step Convert Units

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 200Pa \cdot 10m³ \cdot ({(\frac{700000Pa}{200Pa})}^{\frac{1.2 - 1}{1.2}} + {(\frac{1.5E+6Pa}{700000Pa})}^{\frac{1.2 - 1}{1.2}} - 2)

Next Step Prepare to Evaluate

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 200 \cdot 10 \cdot ({(\frac{700000}{200})}^{\frac{1.2 - 1}{1.2}} + {(\frac{1.5E+6}{700000})}^{\frac{1.2 - 1}{1.2}} - 2)

Next Step Evaluate

∴

w t = 36383.6804327J

LAST Step Rounding Answer

∴

w t = 36383.6804J

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Formula Elements

Variables

Total Work Done per Cycle

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.

Symbol: w_t

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

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.

Symbol: n_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Suction Pressure of Low Pressure Compressor

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.

Symbol: P₁

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Suction Volume

Suction volume is the volume of air drawn into the compressor's cylinder during the suction stroke of the compression process.

Symbol: V₁

Measurement: VolumeUnit: m³

Note: Value can be positive or negative.

Discharge Pressure of Low Pressure Compressor

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.

Symbol: P₂

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Discharge Pressure of High Pressure Compressor

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.

Symbol: P₃

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Credits

Created by Abhishek Dharmendra Bansile

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

Abhishek Dharmendra Bansile has created this Formula and 100+ more formulas!

Verified by

national institute of technology hamirpur (NITH ), Hamirpur, Himachal Pradesh

sanjay shiva has verified this Formula and 100+ more formulas!

Other Formulas to find Total Work Done per Cycle

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

w t = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot ((T 1 \cdot {(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}}) + T 3 \cdot {(\frac{P 3}{P 2})}^{\frac{n c - 1}{n c}} - T 1 - T 3)

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

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)

Go Total Work done per cycle in Compressor during Complete Intercooling given Suction Volume

w t = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T 1 \cdot ({(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}} + {(\frac{P 3}{P 2})}^{\frac{n c - 1}{n c}} - 2)

Other formulas in Work Done by Two Stage Compressor category

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

w = (\frac{n c}{n c - 1}) \cdot P 1 \cdot V 1 \cdot ({(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}} - 1)

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

w = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T 1 \cdot ({(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}} - 1)

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

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

Go Work done per cycle in High Pressure Compressor during incomplete intercooling given suction Temp

w = (\frac{n c}{n c - 1}) \cdot m \cdot [R] \cdot T 2 \cdot ({(\frac{P 3}{P 2})}^{\frac{n c - 1}{n c}} - 1)

How to Evaluate Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature?

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature evaluator uses 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) to evaluate the Total Work Done per Cycle, Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature formula is defined as the energy transferred per cycle in a two-stage compressor with complete intercooling, considering the suction temperature, and is a crucial parameter in evaluating the compressor's performance and efficiency. Total Work Done per Cycle is denoted by w_t symbol.

How to evaluate Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature using this online evaluator? To use this online evaluator for Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature, enter Polytropic Index for Compression (n_c), Suction Pressure of Low Pressure Compressor (P₁), Suction Volume (V₁), Discharge Pressure of Low Pressure Compressor (P₂) & Discharge Pressure of High Pressure Compressor (P₃) and hit the calculate button.

FAQs on Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature

What is the formula to find Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature?

The formula of Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature is expressed as 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). Here is an example- 36383.68 = (1.2/(1.2-1))*200*10*((700000/200)^((1.2-1)/1.2)+(1500000/700000)^((1.2-1)/1.2)-2).

How to calculate Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature?

With Polytropic Index for Compression (n_c), Suction Pressure of Low Pressure Compressor (P₁), Suction Volume (V₁), Discharge Pressure of Low Pressure Compressor (P₂) & Discharge Pressure of High Pressure Compressor (P₃) we can find Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature using the formula - 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).

What are the other ways to Calculate Total Work Done per Cycle?

Here are the different ways to Calculate Total Work Done per Cycle-

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))*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=(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)

Can the Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature be negative?

Yes, the Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature, measured in Energy can be negative.

Which unit is used to measure Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature?

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature can be measured.

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Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Formula

​GoTotal Work done per cycle in Compressor during incomplete Intercooling given Temperature Formula

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

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Example

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Solution

Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature Formula Elements

Credits

Other Formulas to find Total Work Done per Cycle

Other formulas in Work Done by Two Stage Compressor category

How to Evaluate Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature?

FAQs on Total Work done per cycle in Compressor during Complete Intercooling given Suction Temperature

Variable Name

GoTotal Work done per cycle in Compressor during incomplete Intercooling given Temperature Formula

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