- #1

- 56

- 6

- Homework Statement
- Derive the equation of state for an ideal gas that relates pressure, density, and temperature.

- Relevant Equations
- 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.

$$

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.