AZING!What is the Polytopic Index for a given set of Pressure and Volume values?

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In summary, the conversation discusses finding the value of n in the equation PV^n=constant, with given values for P1, P2, V1, and V2. The individual has attempted to use logarithms to solve for n but is struggling to isolate the variable. They seek help from others and provide their attempted solution using logarithms.
  • #1
tsukuba
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Homework Statement


Hello, I came across a problem where the polytropic index is not given but I've been given P1, P2, V1 and V2.

P1V1 = P2V2 (130kPa)(0.007m3)n = (100kPa)(0.08637m3)n ----> n=1.249

Homework Equations


PVn=constant
I was thinking I would have to use log to figure out n maybe?

The Attempt at a Solution


haven't been able to work it out backwards. Need your help please!
 
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  • #2
tsukuba said:
I was thinking I would have to use log to figure out n maybe?
If xn = k then ln(xn) = ln(k)AM
 
  • #3
the value of n is not given. I just put it there because but what if it was
xn = ?
solving for n
 
  • #4
somebody helpppp
I have a test tomorrow
 
  • #5
I came to this but now I am not sure how to isolate for n

ln(130) n*ln(0.07) = ln(100) n*ln90.08637)
 
  • #6
tsukuba said:
I came to this but now I am not sure how to isolate for n

ln(130) n*ln(0.07) = ln(100) n*ln90.08637)

[tex]P_1V_1^n = P_2V_2^n[/tex]
[tex]\frac{P_1}{P_2} = \left(\frac{V_2}{V_1}\right)^n[/tex]
[tex]\ln(P_1)-\ln(P_2) = n(\ln(V_2) - \ln(V_1))[/tex]

Can you work it out from there?

AM
 

FAQ: AZING!What is the Polytopic Index for a given set of Pressure and Volume values?

What is boundary work in thermodynamics?

Boundary work in thermodynamics refers to the work done by a system as it expands or compresses against a constant external pressure. It is a form of mechanical work that occurs at the boundary between the system and its surroundings.

How is boundary work calculated?

Boundary work is calculated by multiplying the external pressure by the change in volume of the system. This can be represented by the equation W = PΔV, where W is the boundary work, P is the external pressure, and ΔV is the change in volume.

What is the difference between boundary work and other forms of work?

Boundary work is a specific type of mechanical work that occurs at the boundary of a system, while other forms of work, such as shaft work or flow work, occur within the system. Boundary work is also dependent on the external pressure, while other forms of work may not be affected by external factors.

What is the significance of boundary work in thermodynamics?

Boundary work is an important concept in thermodynamics as it allows us to understand the energy exchange that occurs between a system and its surroundings. It is also a key factor in determining the efficiency of processes and the maximum possible work that can be obtained from a system.

Can boundary work be negative?

Yes, boundary work can be negative if the system is compressed by an external pressure. This means that work is being done on the system, and energy is being transferred from the surroundings to the system. In contrast, positive boundary work occurs when the system expands and does work on the surroundings.

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