# Why is the force due to a vacuum in a syringe so much greater than the force due to the air being compressed in the syringe?

I'm a teacher using a plastic syringe (no needle) to demonstrate the compressibility of air and the incompressibility of water. Works great, they can push the plunger in while blocking the end of the syringe when there is air in the syringe, but not when the syringe is filled with water. We note that the syringe returns to its original position as the high pressure air in the syringe pushes the plunger out against atmospheric pressure. It's fairly slow moving but it does return to the original position. But then one student blocks the end and pulls the plunger out. This time when he lets go the plunger shoots back in. I am now at a loss to explain why the speed of the plunger is so much greater. So back at home I try to calculate the forces. I'm using the rule that pressure is inversely proportional to volume at the same temperature. If the volume of the syringe is reduced by a factor of 4, then the pressure inside the syringe will be four times bigger than atmospheric pressure. So the force on the plunger will be 4PA outwards and PA inwards (where P is atmospheric pressure and A is the area of the plunger.) This will give a resultant force of 3PA pushing the plunger out. Now consider the opposite case where the volume of the syringe is increased by a factor of 4. Now the pressure inside the syringe is P/4, and outside is still P. So the forces are PA/4 outwards and PA inwards. This gives a resultant force of 3/4 PA. That is a much smaller resultant force when the plunger is pulled out than when the plunger is pushed in. So how come the plunger moves so much faster when it is let go after pulling it out?

• Regarding your credibility as a science teacher, the most scientific approach you could possibly take is to first (cheerfully!) admit that you don't know the answer to this puzzle, and then to do your best to solve it (either via consultation or your own experiments). The lessons that not knowing is not the same as stupidity, and that being ashamed of not knowing actively prevents us from learning the truth, is IMO the greatest gift you could possibly give a student. After all, a good scientist is excited by a new puzzle, not embarrassed by not immediately knowing the solution. Dec 7, 2021 at 12:27

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.

• Thank you for your answer. I'm interested in the idea that this is an adiabatic process, so the air pressure would be less when the plunger is pulled out due to the drop in temperature. But this would work the other way when the plunger is pushed in, increasing the temperature so the pressure would be higher than otherwise expected. So even though this process may be at work it would not explain the difference between pushing and pulling the plunger. Dec 6, 2021 at 1:05

The only thing I can imagine is the the force of friction is different.

Perhaps the piston gets twists a bit when you push it in, but not when you pull it out. If so, it would push harder on the side of the cylinder and move slower. This doesn't sound very likely, but it is the direction I would look for problems.

Perhaps the inside of the cylinder has dirt in it at one end but not the other. Dirt could cause friction.

You might try cleaning or lubricating the syringe to see of that makes a difference.

Perhaps the cylinder is not of uniform diameter. It would travel slower where a slight constriction is.

Perhaps the piston has asymmetric o-rings or other seals. They might dig in in one direction, but not the other.

Further thought - You might try it without the piston to see if the problem persists.

Get a turkey baster and a fish tank. Remove the bulb from the baster.

Plug the tip with your finger and push the open end deep into the water. The tube is full of air. Release your finger and see how quickly water rises in the tube.

With the tip uncovered, push the open end deep into the water. The tube is full of water. Pull the tube up, leaving the base under water. Release your finger and see how quickly water drops in the tube.

If the problem persists with the new syringe, try lubricating with a drop of oil.

• The syringe design is a very simple one, you can obtain one free at any pharmacy to measure out liquid medicine. Without blocking the end, there is no noticeable difference between pushing and pulling. But maybe the plunger does not travel straight when air pressure pushes it out. I will get a new syringe and try again, my current one is too leaky now to hold a pressure either way. Dec 6, 2021 at 1:15

There are three forces in play:

• the pressure of the air inside the syringe
• the pressure outside the syringe
• the friction between the plunger and the barrel

Expansion of compressed syringe
The expansion of the comressed syringe is thus not strictly speaking isothermal: the compressed air does work against the external pressure and also against the friction force: $$P_{in} A = P_{out}A + F_f,$$ where $$P_{in/out}$$ are the pressures inside and outside of the syringe, $$A$$ is the cross-section area of the plunger, and $$F_f$$ is the friction force. The work against the friction force is done at the expense of the internal energy of the air inside, that is the gas quickly cools, the pressure drops and it cannot push anymore against the plunger. This loss of energy is however replenished via the heat exchange with the surroundings. As a result of balance between energy loss to overcoming frection and heat exchange with the surroundings, the temperature of the air inside remains constant and we can apply the ideal gas law, $$P_1V_1=P_2V_2$$. The process is however not reversible - i.e., not isothermal in the sense of basic thermodynamics books.

The expansion is thus controlled by the speed of the heat exchange between the air inside the syringe and the surroundings. Since these are made of plastic, this is quite slow. I suggest performing the same experiment with an old-fashined glass cyringe - the observations are likely to be different. Note also that the cylindres in internal combustion engine are metallic, i.e., good heat conductors.

Compression of an extended syringe
In this case the work against the friction is done by the external air, and the energy loss due to work against friction is restored via convection.

Remark: The other answers have pointed out that the friction force in a syringe is likely not the same in the two directions, by design. I think that this is an important factor as well.

I was looking at this and using a syringe and came to this conclusion.

When you compress the air and let go the compressed air vs outside air drops as the syringe moves backwards so it decelerates until it is even.

However the "vacuum" vs outside air is constant so it will continue accelerating until it reaches the end