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

GoWork done by Reciprocating Compressor given Suction Temperature Formula

GoWork Done given Polytropic Index for Compression and Expansion 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 - V 4)) \cdot ({(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}} - 1)

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

Work Done by Reciprocating Compressor given Volume before Compression and after Expansion Example

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Here is how the Work Done by Reciprocating Compressor given Volume before Compression and after Expansion equation looks like with Values.

Here is how the Work Done by Reciprocating Compressor given Volume before Compression and after Expansion equation looks like with Units.

Here is how the Work Done by Reciprocating Compressor given Volume before Compression and after Expansion equation looks like.

740324.8322 = (\frac{1.3}{1.3 - 1}) \cdot (1.013 \cdot (3.36 - 0.6)) \cdot ({(\frac{8}{1.013})}^{\frac{1.3 - 1}{1.3}} - 1)

740324.8322J = (\frac{1.3}{1.3 - 1}) \cdot (1.013Bar \cdot (3.36m³ - 0.6m³)) \cdot ({(\frac{8Bar}{1.013Bar})}^{\frac{1.3 - 1}{1.3}} - 1)

740324.8322 = (\frac{1.3}{1.3 - 1}) \cdot (1.013 \cdot (3.36 - 0.6)) \cdot ({(\frac{8}{1.013})}^{\frac{1.3 - 1}{1.3}} - 1)

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Work Done by Reciprocating Compressor given Volume before Compression and after Expansion Solution

Follow our step by step solution on how to calculate Work Done by Reciprocating Compressor given Volume before Compression and after Expansion?

FIRST Step Consider the formula

w = (\frac{n c}{n c - 1}) \cdot (P 1 \cdot (V 1 - V 4)) \cdot ({(\frac{P 2}{P 1})}^{\frac{n c - 1}{n c}} - 1)

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

w = 740324.832197332J

LAST Step Rounding Answer

∴

w = 740324.8322J

Work Done by Reciprocating Compressor given Volume before Compression and after 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