# Modeling Syringes e.g. with the ideal gas law

Gentlemen I have a similar yet very practical problem that might provide further insight. I'm trying to model a moving plunger in a syringe (something like a piston in a cylinder). At time zero the plunger is at rest, the pressure (behind the plunger) is atmosphere and the volume zero. Then I open (hydrogen) gas which flows at a certain flow rate (which varies in time) and the pressure to move the plunger also varies in time. So my idea is to model using:

$$\frac{\mathrm{d}}{\mathrm{d}t}(PV)=\frac{\mathrm{d}}{\mathrm{d}t}RT≡P\frac{\mathrm{d}V}{\mathrm{d}t}+V\frac{\mathrm{d}P}{\mathrm{d}t}=R\frac{\mathrm{d}T}{\mathrm{d} t}$$

If I assume constant temperature $P\frac{\mathrm{d}V}{\mathrm{d}t}+V\frac{\mathrm{d}P}{\mathrm{d} t}=RT$

Is this right?

How do I go about solving this if I know the change in flow rate and pressure versus time?

Note also that as the volume of gas increases so does m (the mass)....I'm puzzled...has anyone every modeled a syringe in detail?

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if you assume constant temperature, then you will have $R\frac{dT}{dt}=0$ – Danu Sep 25 '13 at 10:56
It isn't clear what you're trying to model. Are you assuming a known pressure of the hydrogen gas outside the cylinder, a known mass flow rate into the cylinder, or something else? – John Rennie Sep 25 '13 at 11:02
Thks The syringe plunger is moved by applying a pressure to the back face. On the front face there is a liquid (not a gas). For the time being I just focusing on modeling the gas pushing on the back face of the plunger. At time zero the plunger is at rest and the gas volume and pressure are zero. Then I open the gas flow that varies in time and also does the pressure. The syringe (about 12mm internal diameter) will move very slowly (45mm in 15mins). I consider the gas temperature constant. I have the gas flow and pressure versus time (derived by experimentation). The gas is hydrogen. D. – David Sep 26 '13 at 15:23
More info.....I'm still struggling so please dont forget me. I found this link very useful: homepages.wmich.edu/~dschreib/Courses/Chem430/RvPDff2.htm – David Oct 4 '13 at 12:48