# Pressure as a function of time

1. Nov 23, 2012

### Saitama

1. The problem statement, all variables and given/known data
Find the pressure of air in a vessel being evacuated as a function of evacuation time t. The vessel volume is V, the initial pressure is po. The process is assumed to be isothermal, and the evacuation rate equal to C and independent of pressure.
Note: The evacuation rate is the gas volume being evacuated per unit time, with that volume being measured under the gas pressure attained by that moment.

2. Relevant equations

3. The attempt at a solution
By the ideal gas equation,
pV=nRT
$$\frac{dp}{dt}=\frac{RT}{V}\frac{dn}{dt}$$
$$\frac{dp}{dt}=\frac{RT}{MV}\frac{dm}{dt}$$
where m is the mass of gas in the vessel and M is the molar mass of the gas.

Now i am stuck here, i don't know what to do next.

2. Nov 23, 2012

### TSny

The process removes C units of volume of gas each second. If C units of volume are removed at pressure P and temperature T, how many moles are removed?

3. Nov 23, 2012

### Saitama

$\frac{PC}{RT}$ ?

4. Nov 23, 2012

### TSny

Yes. Use this for dn/dt in your diff eq. [Edit: think about the sign of dn/dt]

Last edited: Nov 23, 2012
5. Nov 23, 2012

### Saitama

$$\frac{dn}{dt}=-\frac{PC}{RT}$$
(Negative sign because the moles keeps on decreasing)
$$\frac{dp}{dt}=\frac{RT}{V}\frac{-PC}{RT}$$
$$\frac{dp}{dt}=\frac{-PC}{V}$$
Solving this, i get the right answer. Thanks a lot TSny!