Undergrad Ideal Gas Law and Differentiation

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The discussion explores the possibility of calculating the rate of change of the number of moles (n) in the Ideal Gas Law, given constant volume (V) and known rates of change for pressure (P) and temperature (T). It emphasizes that while R and V are constants, n must vary over time for the differentiation to be applicable. The formula $$\frac{d\ln{n}}{dt}=\frac{d\ln{P}}{dt}-\frac{d\ln{T}}{dt}$$ is presented as a method for this calculation. It is noted that the value of n must be known at the specific moment of interest. Overall, the discussion confirms that differentiation can be used to relate these variables under certain conditions.
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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