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Work Done given Polytropic Index for Compression and Expansion Formula

GoWork Done by Reciprocating Compressor given Volume before Compression and after Expansion Formula

GoWork done by Reciprocating Compressor given Suction Temperature Formula

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Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source. Check FAQs

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) - (\frac{n e}{n e - 1}) \cdot P 1 \cdot V 4 \cdot ({(\frac{P 2}{P 1})}^{\frac{n e - 1}{n e}} - 1)

w - Work Done Per Cycle?n_c - Polytropic index of Compression?P₁ - Suction Pressure?V₁ - Total Volume of Refrigerant in Compressor?P₂ - Discharge Pressure of Refrigerant?n_e - Polytropic Index of Expansion?V₄ - Expanded Clearance Volume?

Work Done given Polytropic Index for Compression and Expansion Example

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Here is how the Work Done given Polytropic Index for Compression and Expansion equation looks like with Values.

Here is how the Work Done given Polytropic Index for Compression and Expansion equation looks like with Units.

Here is how the Work Done given Polytropic Index for Compression and Expansion equation looks like.

751318.6428 = (\frac{1.3}{1.3 - 1}) \cdot 1.013 \cdot 3.36 \cdot ({(\frac{8}{1.013})}^{\frac{1.3 - 1}{1.3}} - 1) - (\frac{1.2}{1.2 - 1}) \cdot 1.013 \cdot 0.6 \cdot ({(\frac{8}{1.013})}^{\frac{1.2 - 1}{1.2}} - 1)

751318.6428J = (\frac{1.3}{1.3 - 1}) \cdot 1.013Bar \cdot 3.36m³ \cdot ({(\frac{8Bar}{1.013Bar})}^{\frac{1.3 - 1}{1.3}} - 1) - (\frac{1.2}{1.2 - 1}) \cdot 1.013Bar \cdot 0.6m³ \cdot ({(\frac{8Bar}{1.013Bar})}^{\frac{1.2 - 1}{1.2}} - 1)

751318.6428 = (\frac{1.3}{1.3 - 1}) \cdot 1.013 \cdot 3.36 \cdot ({(\frac{8}{1.013})}^{\frac{1.3 - 1}{1.3}} - 1) - (\frac{1.2}{1.2 - 1}) \cdot 1.013 \cdot 0.6 \cdot ({(\frac{8}{1.013})}^{\frac{1.2 - 1}{1.2}} - 1)

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Work Done given Polytropic Index for Compression and Expansion Solution

Follow our step by step solution on how to calculate Work Done given Polytropic Index for Compression and Expansion?

FIRST Step Consider the formula

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) - (\frac{n e}{n e - 1}) \cdot P 1 \cdot V 4 \cdot ({(\frac{P 2}{P 1})}^{\frac{n e - 1}{n e}} - 1)

Next Step Substitute values of Variables

∴

w = (\frac{1.3}{1.3 - 1}) \cdot 1.013Bar \cdot 3.36m³ \cdot ({(\frac{8Bar}{1.013Bar})}^{\frac{1.3 - 1}{1.3}} - 1) - (\frac{1.2}{1.2 - 1}) \cdot 1.013Bar \cdot 0.6m³ \cdot ({(\frac{8Bar}{1.013Bar})}^{\frac{1.2 - 1}{1.2}} - 1)

Next Step Convert Units

∴

w = (\frac{1.3}{1.3 - 1}) \cdot 101300Pa \cdot 3.36m³ \cdot ({(\frac{800000Pa}{101300Pa})}^{\frac{1.3 - 1}{1.3}} - 1) - (\frac{1.2}{1.2 - 1}) \cdot 101300Pa \cdot 0.6m³ \cdot ({(\frac{800000Pa}{101300Pa})}^{\frac{1.2 - 1}{1.2}} - 1)

Next Step Prepare to Evaluate

∴

w = (\frac{1.3}{1.3 - 1}) \cdot 101300 \cdot 3.36 \cdot ({(\frac{800000}{101300})}^{\frac{1.3 - 1}{1.3}} - 1) - (\frac{1.2}{1.2 - 1}) \cdot 101300 \cdot 0.6 \cdot ({(\frac{800000}{101300})}^{\frac{1.2 - 1}{1.2}} - 1)

Next Step Evaluate

∴

w = 751318.642818291J

LAST Step Rounding Answer

∴

w = 751318.6428J

Work Done given Polytropic Index for Compression and Expansion Formula Elements

Variables

Work Done Per Cycle

Work Done per cycle is the total amount of heat absorbed per cycle by the working substance from the source.

Symbol: w

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Work Done Per Cycle

Polytropic index of Compression

Polytropic index of compression is a parameter that defines the relationship between pressure and volume during a thermodynamic process. It indicates how heat is transferred during compression.

Symbol: n_c

Measurement: NAUnit: Unitless