Question

Consider the following apparatus: a test tube covered with a nonpermeable elastic membrane inside a container that is closed with a cork. A syringe goes through the cork. a. As you push down on the syringe, how does the membrane covering the test tube change? b. You stop pushing the syringe but continue to hold it down. In a few seconds, what happens to the membrane?

Short answer

a. As you push down on the syringe, the elastic membrane covering the test tube stretches and expands due to the increased pressure inside the container. b. When you stop pushing the syringe but continue to hold it down, the pressure equalizes inside and outside the test tube, causing the membrane to stabilize at a new position (still expanded compared to the initial position). It will remain unchanged as long as the pressure is constant.

Step-by-step solution

Understand the initial setup

The test tube with a nonpermeable elastic membrane is inside a container closed with a cork. The syringe is going through the cork, and initially, we have not applied any force on the syringe.

Analyze the effect of pushing down on the syringe (Part a)

As you push down on the syringe, you are increasing the pressure inside the container. This increased pressure will cause the elastic membrane to stretch and expand. The reason is that the membrane will try to balance the pressure inside and outside the test tube.

Describe the change in the membrane in Part a

When you push down on the syringe, the elastic membrane covering the test tube will stretch and expand to cope with the increased pressure inside the container.

Analyze the effect of holding the syringe down (Part b)

After pushing down the syringe, you stop pushing but continue to hold it down, maintaining the increased pressure. In a few seconds, the pressure in the container has an opportunity to equalize.

Describe the change in the membrane in Part b

When the pressure equalizes inside and outside the test tube, the membrane will stabilize at a new position (still expanded compared to the initial position). It will no longer change as long as the pressure is held constant by holding the syringe down.

Key concepts

Pressure Equalization

When we talk about pressure equalization in a closed system, such as the one described in the exercise with the test tube and syringe, we are referring to the natural phenomenon where pressure seeks to become uniform throughout the entire system.

In the experiment, pushing down on the syringe increases the pressure within the container because we are compressing the air inside it. Initially, the increased pressure is not uniform throughout the container. Nature, however, abhors a gradient, so the system will attempt to even out the pressure discrepancies. This process is called pressure equalization, and it happens as the air molecules move around and collide, redistributing their energy until a steady state is achieved.

If you stopped pushing the syringe but kept it depressed, as in the experiment, you would have created a new pressure level in the system that would eventually become uniform. This explains why the membrane stabilizes after a few seconds; the pressure inside the container has balanced with the pressure exerted by the stretched membrane.

Nonpermeable Membranes

A nonpermeable membrane acts as a barrier that does not allow substances to pass through it. In our specific context, it means that air molecules cannot move in or out of the test tube covered by the membrane.

When pressure inside the container is increased by the syringe, the nonpermeable membrane's inability to let air pass through means that the only way to balance the pressure differences is by stretching. This is fundamental to the experiment because it limits the ways in which the system can achieve pressure equalization. The rigidity or elasticity of the membrane affects how the pressure difference will be resolved – either by distorting as seen in elastic materials, adhering tightly to the tube if it's non-elastic, or potentially breaking if the applied pressure exceeds the membrane's material strength.

Understanding the properties of nonpermeable membranes can be crucial in fields like medicine and chemical engineering, where selective permeability is often needed to control the flow of substances in a controlled environment.

Effects of Pressure on Elastic Materials

Elastic materials, such as the membrane covering the test tube in our experiment, have the ability to stretch and deform under pressure. This is due to their molecular structure, which allows them to absorb energy—like increased air pressure—by altering shape rather than breaking.

Pushing down on the syringe increases the pressure within the container, as mentioned earlier, and the elastic membrane stretches in response to this change. Ideally, the material will return to its original shape once the pressure is removed; this is known as elastic deformation. However, if the pressure becomes too great, or is applied for too long, some materials may reach a point of plastic deformation, where they will not return to their original shape.

In practical applications, the understanding of how pressure affects elastic materials is vital. For instance, designers of sports equipment, vehicle tires, and medical devices must take into account the elasticity to ensure that the materials can withstand the stresses they will encounter without failing.