Thermodynamics: Polytropic Process

In summary, using the relevant equations, the initial temperature and final pressure were calculated to be 348.43 K and 3674.23 kPa, respectively. The work done during the process was found to be -43.48 kJ. It is important to use units in calculations and provide some explanation of the equations used to better demonstrate understanding.
  • #1
JasonHathaway
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Homework Statement



Q1- 0.15 kg of air (Ideal) compressed in a polytropic process (PV1.5=C) from 0.06 m3 to 0.01 m3. If the initial pressure was 0.25 MPa. Determine:

1- The initial temperature and the final pressure.

2- The work done during the process.

Homework Equations



P1 V1 = m R T
P1 V11.5= P2V21.5=C
W1-2= (P2V2 - P1V1)/(1-n)

The Attempt at a Solution



P2= P1(V1/V2)1.5= 0.25*103(0.06/0.01)1.5

P2=3674.23 kPa --> The final pressure

T1= (P1V1)/(mR)=(0.25*103*0.06)/(0.15*0.287)

T1=348.43 K --> The initial temperature

W1-2= (P2V2 - P1V1)/(1-n) = (3674.23*0.01 - 0.25*103*0.06)/(1-1.5)

W1-2= -43.48 Kj --> The work during the process
 
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  • #2


it is important to approach any problem with a systematic and logical approach. In this case, you have correctly identified the relevant equations and used them to find the values for the initial temperature, final pressure, and work done during the process. Your calculations appear to be correct and your final answers are in the correct units.

One suggestion for improvement would be to include units in your calculations, as this can help to avoid errors and make your work more clear. Additionally, it may be helpful to provide a brief explanation of the equations you are using and how you are applying them to solve the problem. This can help to demonstrate your understanding of the concepts and can also make your response more informative for others who may be reading it.

Overall, your response is clear and concise, and it effectively answers the questions posed in the forum post. Great job!
 

1. What is a polytropic process in thermodynamics?

A polytropic process in thermodynamics is a type of thermodynamic process where there is a relationship between pressure and volume, expressed as PVn = constant. This means that the process follows a specific power law, with the exponent n determining the type of process (e.g. isobaric, isochoric, isothermal, adiabatic).

2. How does a polytropic process differ from other thermodynamic processes?

Unlike other thermodynamic processes, a polytropic process does not have a fixed pressure or volume. Instead, the relationship between pressure and volume is expressed as a power law, allowing for variations in these properties throughout the process.

3. What is the significance of a polytropic process in thermodynamics?

A polytropic process is significant because it allows for a more accurate representation of real-world processes, where pressure and volume may not be constant. It also allows for a more flexible analysis of thermodynamic systems, as it can describe a range of processes depending on the value of the exponent n.

4. How is work calculated in a polytropic process?

In a polytropic process, work is calculated as the area under the PV curve. This can be done using the polytropic expansion or compression formula, which takes into account the specific value of the exponent n.

5. Can a polytropic process occur in a closed system?

Yes, a polytropic process can occur in a closed system. In fact, many real-world processes, such as the expansion or compression of a gas in an engine, can be approximated as polytropic processes. However, in a closed system, the exponent n must be constant for the entire process, whereas in an open system it can vary.

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