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Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula

GoMinimum Work required when Temperature at end of Cooling in Intercooler is fixed Formula

GoMinimum Work required when Cooling Ratio is fixed Formula

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Work required means work that is necessary in order to provide a covered service sought in connection application. Check FAQs

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

W - Work Required?n_c - Polytropic Index For Compression?m - Mass of Refrigerant in kg Per Minute?T_r - Suction Temperature of Refrigerant?P₃ - Discharge Pressure of High Pressure Compressor?P₁ - Suction Pressure of Low Pressure Compressor?[R] - Universal gas constant?

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Example

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Here is how the Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect equation looks like with Values.

Here is how the Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect equation looks like with Units.

Here is how the Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect equation looks like.

50.7564 = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0304 \cdot 8.3145 \cdot 940 \cdot ({(\frac{15}{0.0024})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

50.7564J = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0304kg/min \cdot 8.3145 \cdot 940K \cdot ({(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

50.7564 = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0304 \cdot 8.3145 \cdot 940 \cdot ({(\frac{15}{0.0024})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

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Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Solution

Follow our step by step solution on how to calculate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

W = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0304kg/min \cdot [R] \cdot 940K \cdot ({(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

Next Step Substitute values of Constants

∴

W = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0304kg/min \cdot 8.3145 \cdot 940K \cdot ({(\frac{15Bar}{0.0024Bar})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

Next Step Convert Units

∴

W = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0005kg/s \cdot 8.3145 \cdot 940K \cdot ({(\frac{1.5E+6Pa}{243Pa})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

Next Step Prepare to Evaluate

∴

W = 2 \cdot (\frac{1.2}{1.2 - 1}) \cdot 0.0005 \cdot 8.3145 \cdot 940 \cdot ({(\frac{1.5E+6}{243})}^{\frac{1.2 - 1}{2 \cdot 1.2}} - 1)

Next Step Evaluate

∴

W = 50.7563853415876J

LAST Step Rounding Answer

∴

W = 50.7564J

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula Elements

Variables

Constants

Work Required

Work required means work that is necessary in order to provide a covered service sought in connection application.

Symbol: W

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Work Required

Polytropic Index For Compression

Polytropic Index For Compression is that defined via a polytropic equation of state of the form P∝ρ1+1/n, where P is pressure, ρ is density, and n is the polytropic index.

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 the mass on or by which the work is done.

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 of Refrigerant

The Suction temperature of refrigerant is the temperature of refrigerant at inlet or during the suction stroke.

Symbol: T_r

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Suction Temperature of Refrigerant

Discharge Pressure of High Pressure Compressor

Discharge Pressure of High Pressure Compressor is the pressure of the refrigerant at the point where it exits the High Pressure compressor. It is also called Condenser Pressure.

Symbol: P₃

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Discharge Pressure of High Pressure Compressor

Suction Pressure of Low Pressure Compressor

Suction Pressure of Low Pressure Compressor is the pressure of the refrigerant at the point where it enters the Low pressure compressor. It is also called Evaporator pressure.

Symbol: P₁

Measurement: PressureUnit: Bar

Note: Value can be positive or negative.

Formulas to find Suction Pressure of Low 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 Work Required

Go Minimum Work required when Temperature at end of Cooling in Intercooler is fixed

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

Go Minimum Work required when Cooling Ratio is fixed

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

Other formulas in Minimum Work category

Go Cooling ratio

q = \frac{T 2 - T 3}{T 2 - T 1}

Go Discharge Temperature at High Pressure Compressor given Cooling Ratio

T 3 = T 2 - q \cdot (T 2 - T 1)

Go Suction Temperature at Low Pressure Compressor given Cooling Ratio

T 1 = \frac{(T 2 \cdot q) - T 2 + T 3}{q}

Go Discharge Temperature at High pressure compressor when Cooling ratio is constant

T 3 = P 1 \cdot (q + (1 - q) \cdot {(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}})

How to Evaluate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect evaluator uses Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1) to evaluate the Work Required, Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect formula is defined as the minimum energy required to cool a refrigerant in a perfect intercooling system with a fixed cooling ratio, which is a critical parameter in refrigeration systems. Work Required is denoted by W symbol.

How to evaluate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect using this online evaluator? To use this online evaluator for Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect, enter Polytropic Index For Compression (n_c), Mass of Refrigerant in kg Per Minute (m), Suction Temperature of Refrigerant (T_r), Discharge Pressure of High Pressure Compressor (P₃) & Suction Pressure of Low Pressure Compressor (P₁) and hit the calculate button.

FAQs on Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect

What is the formula to find Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

The formula of Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect is expressed as Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1). Here is an example- 30.13525 = 2*(1.2/(1.2-1))*0.000506*[R]*940*((1500000/243)^((1.2-1)/(2*1.2))-1).

How to calculate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

With Polytropic Index For Compression (n_c), Mass of Refrigerant in kg Per Minute (m), Suction Temperature of Refrigerant (T_r), Discharge Pressure of High Pressure Compressor (P₃) & Suction Pressure of Low Pressure Compressor (P₁) we can find Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect using the formula - Work Required = 2*(Polytropic Index For Compression/(Polytropic Index For Compression-1))*Mass of Refrigerant in kg Per Minute*[R]*Suction Temperature of Refrigerant*((Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1). This formula also uses Universal gas constant .

What are the other ways to Calculate Work Required?

Here are the different ways to Calculate Work Required-

Work Required=2*(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 High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-1)
Work Required=(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 High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))+Discharge Temperature of Refrigerant*(Discharge Pressure of High Pressure Compressor/Suction Pressure of Low Pressure Compressor)^((Polytropic Index For Compression-1)/(2*Polytropic Index For Compression))-Suction Temperature at Low Pressure Compressor-Discharge Temperature at High Pressure Compressor))

Can the Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect be negative?

Yes, the Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect, measured in Energy can be negative.

Which unit is used to measure Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect can be measured.

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Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula

​GoMinimum Work required when Temperature at end of Cooling in Intercooler is fixed Formula

​GoMinimum Work required when Cooling Ratio is fixed Formula

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Example

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Solution

Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect Formula Elements

Other Formulas to find Work Required

Other formulas in Minimum Work category

How to Evaluate Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect?

FAQs on Minimum Work required when Cooling Ratio is fixed and Intercooling is Perfect

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GoMinimum Work required when Temperature at end of Cooling in Intercooler is fixed Formula

GoMinimum Work required when Cooling Ratio is fixed Formula