Polytropic Process for an Ideal Gas

  • Thread starter LunaFly
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  • #1
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Hi,

I have a general question about polytropic processes when working with an ideal gas.

A polytropic process is one for which PV[itex]\gamma[/itex] = constant.

What I am wondering is if we assume that n is constant, does that mean that the temperature does not change for the process?

I see that PV[itex]\gamma[/itex] = nrT = constant, but for some reason it doesn't seem right that a polytropic process would be equivalent to an isothermal process if the number of moles of the system doesn't change.

A little light on the subject would be great.

Thanks,

-Luna
 

Answers and Replies

  • #2
DrClaude
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Hi,

I have a general question about polytropic processes when working with an ideal gas.

A polytropic process is one for which PV[itex]\gamma[/itex] = constant.

What I am wondering is if we assume that n is constant, does that mean that the temperature does not change for the process?
No. A good example of such a process is adiabatic expansion/compression, for which ##T## changes.

I see that PV[itex]\gamma[/itex] = nrT
That equation is only valid if ##\gamma = 1##. Otherwise, there is no simple relationship between ##PV^\gamma## and ##T##.
 
  • #3
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Ok this concept finally sunk in.

PV[itex]\gamma[/itex] does not equal nRT unless [itex]\gamma[/itex]=1. So a polytropic process in no way implies that nRT is a constant (even when n is constant).

DrClaude, thanks for the input!
 
  • #4
DrClaude
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Ok this concept finally sunk in.

PV[itex]\gamma[/itex] does not equal nRT unless [itex]\gamma[/itex]=1. So a polytropic process in no way implies that nRT is a constant (even when n is constant).
Another thing to consider that might be helpful for your understanding:

Consider a process for an ideal gas where ##PV^\gamma = \textrm{const.}##. Using the ideal gas law, ##PV=nRT##, we have
$$
\begin{align}
P_iV_i^\gamma &= P_fV_f^\gamma \\
\left( \frac{n R T_i}{V_i} \right) V_i^\gamma &= \left( \frac{n R T_f}{V_f} \right) V_f^\gamma \\
T_i V_i^{\gamma - 1} &= T_f V_f^{\gamma - 1}
\end{align}
$$
or ##TV^{\gamma - 1} = \textrm{const.}##
Obviously, if ##V## changes during the process, then ##T## changes (except if ##\gamma = 1##).
 
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