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Introductory Physics Homework Help
Incompatibility between ideal gas equations of state
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[QUOTE="Portuga, post: 6852520, member: 427847"] [B]Homework Statement:[/B] Derive the equation of state for an ideal gas that relates pressure, density, and temperature. [B]Relevant Equations:[/B] PV = nRT To solve this problem I used two equations: $$ PV=nRT, $$ where ##P## is the pressure, ##V##the volume, ##R##the gas constant, ##T##for temperature and is##n##the number of moles, related to the mass ##m## and molar mass ##M## by $$ n=\frac{m}{M}. $$ It will be also necessary consider the density ##\rho## as $$ \rho=\frac{m}{V}. $$ So, \begin{align} & PV=\frac{m}{M}RT\nonumber \\ \Rightarrow & \frac{P}{\frac{m}{V}}=\frac{RT}{M}\nonumber \\ \Rightarrow & \frac{P}{\rho}=\frac{RT}{M}.\nonumber \end{align} When I checked the answer, to my surprise I found $$ \frac{P}{\rho}=RT. $$ I am so confused because this is so simple and I have no idea about what to do with the molar mass##M##to get the answer provided by the author. [/QUOTE]
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Incompatibility between ideal gas equations of state
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