Reversible work of compression

In summary, the problem involves calculating the work done, reversible work, and irreversibility of a compressor with given conditions and an isentropic efficiency of 87%. The work done can be calculated using the formula W = (Cp(T2-T1))/η, where T2, T1, and η are known. The reversible work can be found using the formula Wrev=Δh - T0Δs, where Δh and Δs can be calculated using the equations cpln(T2/T1) and Rln(P2/P1). The correct answers for the work, reversibility, and irreversibility are -338.2 kj/kg, -317.4 kj/kg, and
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Homework Statement


Air enters a compressor at 100 [Kpa] and 10 [c], the air leave the compressor at 12[Mpa]
the isentropic efficiency η is 87%, calculate:
  • work done
  • reversible work
  • irreversibility

Homework Equations


[/B]
T2=T1(P2/P1)(1.4-1)/1.4
W = (Cp(T2-T1))/η
Wrev=Δh - T0Δs
Δs = cpln(T2/T1) - Rln(P2/P1)

The Attempt at a Solution


[/B]
Work done can be calculated with:
T2=T1(P2/P1)(1.4-1)/1.4
W = (Cp(T2-T1))/η
T1 , P1 , P2 are given.
Δs = cpln(T2/T1) - Rln(P2/P1)
I tried to find Wrev with Δh - T0Δs
and Δs = cpln(T2/T1) - Rln(P2/P1)

the correct answers are :
  • work : -338.2 kj/kg
  • reversibility : -317.4 kj/kg
  • irreversibility : 20.8 kj/kg
 
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  • #2
but I can't figure out how to solve this.Can someone please help me with the steps?thanks in advance!
 

FAQ: Reversible work of compression

What is reversible work of compression?

The reversible work of compression refers to the amount of work that is required to compress a gas or fluid back to its original state after it has been expanded. This process is reversible because it can be reversed without causing any changes to the system or its surroundings.

How is reversible work of compression different from irreversible work?

Reversible work of compression is a theoretical concept wherein the compression process is carried out slowly and without any energy losses, while irreversible work is the actual work that is required to compress a gas or fluid in real-world conditions. Reversible work is always lower than irreversible work due to energy losses in the compression process.

What factors affect the reversible work of compression?

The reversible work of compression is affected by various factors such as the initial and final states of the gas or fluid, the temperature and pressure of the system, and the type of compression process (isothermal, adiabatic, etc.). The reversible work also depends on the type of gas or fluid being compressed and its properties.

How is reversible work of compression calculated?

The reversible work of compression can be calculated using the formula W = -PΔV, where W is the work done, P is the pressure of the system, and ΔV is the change in volume. This formula applies for reversible isothermal compression, while for reversible adiabatic compression, the formula is W = -γ/(γ-1) * P1V1 * (V2/V1)^(γ-1), where γ is the adiabatic index and P1 and V1 are the initial pressure and volume, respectively.

What are the practical applications of reversible work of compression?

The concept of reversible work of compression is used in various fields such as thermodynamics, chemical engineering, and mechanical engineering. It helps in understanding the efficiency of compression processes and is used in the design and optimization of compression systems, such as compressors, turbines, and engines. It also has applications in the study of energy conversion and storage systems.

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