Polytropic Process: Finding Final Pressure and Volume

In summary, a frictionless piston cylinder contains ideal gas hydrogen with properties of R = 4.125 KJ/Kg.K and γ= 1.4. The gas undergoes a polytropic process with n = 1.22 from an initial pressure of 100 Kpa, temperature of 765 C, and volume of 0.35 m3 until reaching a final volume of 8.0 m3. To find the mass of the gas and final pressure and volume, the equation PVn = constant can be used.
  • #1
Mohd17
3
0

Homework Statement



A frictionless piston cylinder contains ideal gas hydrogen , R = 4.125 KJ/Kg.K , initially at p1=100 Kpa , t1 = 765 C , V1 = 0.35 m3 . The gas undergoes a polytropic process with n = 1.22 until the final volume becomes V2=8.0 m3

Cp = 14.3338 , Cv= 10.2043 , [URL]http://www.taftan.com/thermodynamics/GAMMA.GIF[/URL] = 1.4

Find :
a) Mass of the ideal gas
b) Final pressure and volume of the gas
 
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  • #2
You need to post your attempt.

What relevant equations do you think are needed here?
 
  • #3
the problem how can i get the volume of the gas !

already i get the answers for part a and the final pressure
 
  • #4
Mohd17 said:
the problem how can i get the volume of the gas !

already i get the answers for part a and the final pressure

You should know for a polytropic process PVn = constant.
 
  • #5
sorry but i didin't understand ...
now what's the answer ?
 
  • #6
Mohd17 said:
sorry but i didin't understand ...
now what's the answer ?

PVn = constant means that

P1V1n = P2V2n

You were given P1, V1, n and you found P2.
 

1. What is a polytropic process?

A polytropic process is a thermodynamic process in which a system undergoes a change in its state, while the relationship between pressure and volume remains constant. This means that the system follows a specific path on a pressure-volume diagram, known as a polytropic curve.

2. What is the equation for a polytropic process?

The equation for a polytropic process is given by: P1V1^n = P2V2^n, where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and n is the polytropic index.

3. What is the polytropic index?

The polytropic index, denoted by n, is a measure of the relationship between pressure and volume during a polytropic process. It is equal to the ratio of specific heats (γ) of the gas, and is often used to characterize the behavior of a gas during a polytropic process.

4. What are some real-life examples of polytropic processes?

Some real-life examples of polytropic processes include the compression or expansion of a gas in a piston-cylinder system, the compression or expansion of air in a turbocharger, and the compression or expansion of gas in a gas turbine. Polytopic processes can also occur in the human body, such as during breathing or blood circulation.

5. How is a polytropic process different from other thermodynamic processes?

A polytropic process differs from other thermodynamic processes in that it maintains a constant relationship between pressure and volume throughout the process. This means that the work done and heat transferred during a polytropic process can be calculated using the same equation, unlike other processes such as isothermal or adiabatic processes.

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