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Total 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

GoTotal Work done per cycle in Compressor during Complete Intercooling given Suction 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 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)

w_t - Total Work Done per Cycle?n_c - Polytropic Index for Compression?m - Mass of Refrigerant in kg per minute?T₁ - Suction Temperature at Low Pressure Compressor?P₂ - Discharge Pressure of Low Pressure Compressor?P₁ - Suction Pressure of Low Pressure Compressor?T₃ - Temperature at Exit of Intercooler?P₃ - Discharge Pressure of High Pressure Compressor?[R] - Universal gas constant?

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

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

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

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

36383.5362 = (\frac{1.2}{1.2 - 1}) \cdot 2 \cdot 8.3145 \cdot ((7216 \cdot {(\frac{7}{0.002})}^{\frac{1.2 - 1}{1.2}}) + 7223 \cdot {(\frac{15}{7})}^{\frac{1.2 - 1}{1.2}} - 7216 - 7223)

36383.5362J = (\frac{1.2}{1.2 - 1}) \cdot 2kg/min \cdot 8.3145 \cdot ((7216K \cdot {(\frac{7Bar}{0.002Bar})}^{\frac{1.2 - 1}{1.2}}) + 7223K \cdot {(\frac{15Bar}{7Bar})}^{\frac{1.2 - 1}{1.2}} - 7216K - 7223K)

36383.5362 = (\frac{1.2}{1.2 - 1}) \cdot 2 \cdot 8.3145 \cdot ((7216 \cdot {(\frac{7}{0.002})}^{\frac{1.2 - 1}{1.2}}) + 7223 \cdot {(\frac{15}{7})}^{\frac{1.2 - 1}{1.2}} - 7216 - 7223)

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

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

FIRST Step Consider the formula

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)

Next Step Substitute values of Variables

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 2kg/min \cdot [R] \cdot ((7216K \cdot {(\frac{7Bar}{0.002Bar})}^{\frac{1.2 - 1}{1.2}}) + 7223K \cdot {(\frac{15Bar}{7Bar})}^{\frac{1.2 - 1}{1.2}} - 7216K - 7223K)

Next Step Substitute values of Constants

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 2kg/min \cdot 8.3145 \cdot ((7216K \cdot {(\frac{7Bar}{0.002Bar})}^{\frac{1.2 - 1}{1.2}}) + 7223K \cdot {(\frac{15Bar}{7Bar})}^{\frac{1.2 - 1}{1.2}} - 7216K - 7223K)

Next Step Convert Units

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 0.0333kg/s \cdot 8.3145 \cdot ((7216K \cdot {(\frac{700000Pa}{200Pa})}^{\frac{1.2 - 1}{1.2}}) + 7223K \cdot {(\frac{1.5E+6Pa}{700000Pa})}^{\frac{1.2 - 1}{1.2}} - 7216K - 7223K)

Next Step Prepare to Evaluate

∴

w t = (\frac{1.2}{1.2 - 1}) \cdot 0.0333 \cdot 8.3145 \cdot ((7216 \cdot {(\frac{700000}{200})}^{\frac{1.2 - 1}{1.2}}) + 7223 \cdot {(\frac{1.5E+6}{700000})}^{\frac{1.2 - 1}{1.2}} - 7216 - 7223)

Next Step Evaluate

∴

w t = 36383.5362339162J

LAST Step Rounding Answer

∴

w t = 36383.5362J

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

Variables

Constants

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.

Formulas to find Total Work Done per Cycle

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.

Formulas to find Polytropic Index for Compression

Mass of Refrigerant in kg per minute

Mass of Refrigerant in kg per minute is defined as the quantity of refrigerant flowing through a system per minute, measured in kilograms.

Symbol: m

Measurement: Mass Flow RateUnit: kg/min

Note: Value should be greater than 0.

Formulas to find Mass of Refrigerant in kg per minute

Suction Temperature at Low Pressure Compressor

Suction temperature at Low pressure Compressor is the temperature of the refrigerant at the suction side of the low-pressure compressor in a two-stage compression system.

Symbol: T₁

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Suction Temperature at Low Pressure Compressor

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.

Formulas to find Discharge Pressure of Low Pressure Compressor

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.

Formulas to find Suction Pressure of Low Pressure Compressor

Temperature at Exit of Intercooler

Temperature at exit of Intercooler is the temperature of the air or gas at the outlet of the intercooler in a two-stage compressor system.

Symbol: T₃

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature at Exit of Intercooler

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.

Formulas to find Discharge Pressure of High Pressure Compressor

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other Formulas to find Total Work Done per Cycle

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)

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

Total Work done per cycle in Compressor during incomplete Intercooling given Temperature evaluator uses 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) to evaluate the Total Work Done per Cycle, Total Work done per cycle in Compressor during incomplete Intercooling given Temperature formula is defined as a measure of the total energy transferred per cycle in a two-stage compressor with incomplete intercooling, considering the temperature and pressure ratios at different stages. Total Work Done per Cycle is denoted by w_t symbol.

How to evaluate Total Work done per cycle in Compressor during incomplete Intercooling given Temperature using this online evaluator? To use this online evaluator for Total Work done per cycle in Compressor during incomplete Intercooling given Temperature, enter Polytropic Index for Compression (n_c), Mass of Refrigerant in kg per minute (m), Suction Temperature at Low Pressure Compressor (T₁), Discharge Pressure of Low Pressure Compressor (P₂), Suction Pressure of Low Pressure Compressor (P₁), Temperature at Exit of Intercooler (T₃) & Discharge Pressure of High Pressure Compressor (P₃) and hit the calculate button.

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

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

The formula of Total Work done per cycle in Compressor during incomplete Intercooling given Temperature is expressed as 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). Here is an example- 36383.76 = (1.2/(1.2-1))*0.0333333333333333*[R]*((7216*(700000/200)^((1.2-1)/1.2))+7223*(1500000/700000)^((1.2-1)/1.2)-7216-7223).

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

With Polytropic Index for Compression (n_c), Mass of Refrigerant in kg per minute (m), Suction Temperature at Low Pressure Compressor (T₁), Discharge Pressure of Low Pressure Compressor (P₂), Suction Pressure of Low Pressure Compressor (P₁), Temperature at Exit of Intercooler (T₃) & Discharge Pressure of High Pressure Compressor (P₃) we can find Total Work done per cycle in Compressor during incomplete Intercooling given Temperature using the formula - 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). This formula also uses Universal gas constant .

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))*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)
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)

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

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

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

Total Work done per cycle in Compressor during incomplete Intercooling given 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 incomplete Intercooling given Temperature can be measured.

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Total 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

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

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

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

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

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 incomplete Intercooling given Temperature?

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

Variable Name

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

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