When you pull the plunger out on a syringe it causes the volume within the chamber to increase?

Several different factors may be involved, but I suspect the main factor has to do with the design of the syringe.

Although I don't know anything about syringe design, one possibility is they are designed to make it easier to push in on the plunger than pull out on it.

Pulling the plunger out loads the syringe. In order to precisely load the dose you would not want to do it too quickly. So perhaps the syringe is designed to pull out slowly.

On the other hand, once the dose is loaded, you would want to make it easier to deliver it. So perhaps the syringe is designed to push in more quickly.

I suggest you check out how hard it is to push and pull on the plunger without blocking the end.

Although it would not alone explain your observation, you should also know that you may be overestimating what the pressure in the syringe was when the student pulled out the plunger and released it.

If the student quickly pulled out the plunger and then immediately released it, instead of allowing the syringe to sit and come into thermal equilibrium with the room air, the pressure in the syringe immediately before releasing it will be less than P/4. Rapidly pulling the plunger would be the equivalent of an adiabatic process (no heat transfer) because there is not enough time for heat to transfer.

Although rapid pulling of the plunger is not a reversible process, one can compare the final pressure for a reversible adiabatic process with a reversible isothermal process. For a reversible adiabatic expansion the initial and final pressures and volumes are related by the equation:

$$P_{1}V_{1}^{\gamma}=P_{2}V_{2}^{\gamma}$$

For air, $\gamma$ =1.4

Then, for $V_{2}=4V_{1}$

$$P_{2}=\frac{1}{16}P_{1}$$

For a reversible isothermal expansion the equation is

$$P_{1}V_{1}=P_{2}V_{2}$$

which means

$$P_{2}=\frac{1}{4}P_1$$

Once again, however, that would not explain the reason for the rapid inward movement of the plunger. So I suspect the main reason may have to do with the syringe design.

Hope this helps.

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