Association Version Question 3-41**
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The piston of a reciprocating compressor draws in air at 278 k and 101.3 kPa (absolute) and compresses it to 324 kPa (absolute); determine the work done by the piston per kilogram of air. What is the work required to compress 1 kg of air in a sealed cylinder using a piston from 101.3 kPa (absolute) to 324 kPa (absolute)? In both cases, it is treated as an adiabatic compressor. Why is W=VdP used to calculate the work done by a compressor, while W=PdV is used to calculate the work done by a piston? I have always used the formula W=PdV when calculating work
In the first case, the volume of gas V in the compressor’s cylinder remains constant, while the pressure P keeps changing; therefore it is Vdp； In the second case, the mass of air is 1 Kg; the compression pressure should remain constant, while the volume of air keeps changing, so it is Pdv.
In both cases, neither the pressure nor the volume is constant; they are constantly changing. Integration is required for the calculation
I had the same question before, and later found the answer in a textbook on thermodynamics. There is a difference between gas compression inside a compressor and gas compression inside a cylinder (one is a steady-flow system, while the other is a closed system). Gas compression inside a compressor obeys the first law of thermodynamics for steady-flow systems: dH = Q + W. Gas compression inside a cylinder follows the first law of thermodynamics for closed systems: dU = Q + W
Then what? Isn’t the formula for work W=-PdV?
The notations Pdv or VdP in the answer are both incorrect; W = vdp + pdv, and both of these values should change. The difference is that in compression of a steady-flow system, the volume is compressed adiabatically, with W = -dH = Cp dt; whereas in a closed system, the volume is compressed adiabatically with W = -dU = -Cv dt. Then, the relationships for adiabatic processes can be used for calculations, where both Cv and Cp are expressed as functions of R