Ideal Gas Law and Differentiation

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Discussion Overview

The discussion revolves around the application of the Ideal Gas Law, specifically examining the relationship between the rate of change of the number of moles (n), pressure (P), and temperature (T) while volume (V) is held constant. Participants explore the feasibility of differentiating the equation PV = nRT to analyze these rates of change.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant questions whether n is assumed to vary over time, implying that the analysis depends on this assumption.
  • Another participant suggests that calculating the rate of change of n with respect to pressure and temperature is possible through differentiation, but notes that n must be known at a specific moment.
  • A mathematical expression is provided, indicating a relationship between the rates of change of n, P, and T.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether n is constant or varies over time, and the discussion includes multiple viewpoints regarding the differentiation approach.

Contextual Notes

The discussion does not clarify the assumptions regarding the constancy of n, nor does it resolve the implications of the mathematical expression provided.

Siddharth Rajvanshi
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Is it possible to calculate the rate of change of n with respect to rate of change of Pressure and rate of change of Temperature with V unknown but constant by PV = nRT?

Rate of change of Pressure and rate of change of temperature can be measured. R and V are constants.
 
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Are you assuming that ##n## varies in time and is not constant ?
 
It seems to be possible with simple differentiation. However 'n' must be known at the point of time.
 

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$$\frac{d\ln{n}}{dt}=\frac{d\ln{P}}{dt}-\frac{d\ln{T}}{dt}$$
 

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