Why Does the Ideal Gas Law Only Have Two Independent Variables?

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Homework Help Overview

The discussion revolves around the Ideal Gas Law and its representation of independent variables within the context of thermodynamics. The original poster questions why the Ideal Gas Law, which includes four variables (pressure, volume, number of particles, and temperature), is said to only have two independent variables when it is categorized as a simple fluid.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the Ideal Gas Law and other equations of state, such as the internal energy equation, to understand the constraints on independent variables. There is a discussion about whether certain variables can be considered dependent under specific conditions.

Discussion Status

Some participants have provided insights regarding the relationship between different equations of state and the implications for independent variables. There is an ongoing exploration of the assumptions made about the conditions under which these equations apply, with no clear consensus reached yet.

Contextual Notes

Participants are examining the implications of using different equations of state and the conditions under which they hold true, such as constant volume or temperature. The original poster references a specific source that outlines the characteristics of simple fluids, which may influence the discussion.

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Homework Statement


http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/7A20B047-A049-44D6-96D2-75602F179856/0/notes_dfnitns.pdf
There it says tht the number of independent variables of a simple fluid is 2 (see the "Complete Specification" section). But the ideal gas law is PV=NkT which has 4 variables, so why are there not 3 independent variables for an ideal gas which is an example of a simple fluid?


Homework Equations





The Attempt at a Solution

 
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There is another equation of state for ideal gases, U=Nc_vT. The constraint from this additional equation reduces the number of independent variables to two.
 
Mapes said:
There is another equation of state for ideal gases, U=Nc_vT. The constraint from this additional equation reduces the number of independent variables to two.

That equation will only work if V is constant.
 
No. Every student of thermo (including me) claims that at first, but no. It applies to all ideal gases under all processes.

EDIT: To give a little more explanation, c_v is a constant. U=Nc_vT is an equation of state that uses that constant; it's not a process subject to constraints. We could just as well write U=N(c_p-R)T.
 
Last edited:

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