# Assumed value of pressure during quasistatic compression

• beefbrisket
In summary: This is a good approximation due to the quasistatic nature of the compression, as the pressure and force are considered to be equal. In summary, the text describes an ideal gas system being compressed by a piston under external force, and states that the force and pressure are equal, resulting in work done on the gas. This is a good approximation due to the quasistatic nature of the compression.
beefbrisket
My text (Ian Ford - Statistical physics) describes an ideal gas system in a piston being quasistatically compressed by a piston head of area $A$ under external force $f$. It assumes the system has a uniform pressure $p$. All good so far. Then it says: "the force $pA$ equals the applied external force $f$" on its way to showing $\text{d}W = -p\text{d}V$. I have some feeling that this seems sound but I cannot explain why. Is this just a good approximation we make due to the quasistatic nature of the compression or some other reason? I think they cannot exactly equal otherwise there would be no work done due to zero net force.

beefbrisket said:
My text (Ian Ford - Statistical physics) describes an ideal gas system in a piston being quasistatically compressed by a piston head of area $A$ under external force $f$. It assumes the system has a uniform pressure $p$. All good so far. Then it says: "the force $pA$ equals the applied external force $f$" on its way to showing $\text{d}W = -p\text{d}V$. I have some feeling that this seems sound but I cannot explain why. Is this just a good approximation we make due to the quasistatic nature of the compression or some other reason? I think they cannot exactly equal otherwise there would be no work done due to zero net force.
If the compression is very slow (quasi static), the force per unit area exerted by the gas on the piston will only be differentially lower than f. So any negative displacement -dx of the piston will result in work -fdx being applied to the gas. But this is just -pdV.

beefbrisket and vanhees71

## 1. What is the assumed value of pressure during quasistatic compression?

The assumed value of pressure during quasistatic compression is the pressure that is used in calculations and simulations to model the behavior of a material under compression. It is typically an average value that is assumed to be constant throughout the compression process.

## 2. Why is the assumed value of pressure important in quasistatic compression?

The assumed value of pressure is important because it allows for simplified calculations and simulations, making it easier to study the behavior of materials under compression. It also helps to establish a baseline for comparison when testing different materials or conditions.

## 3. How is the assumed value of pressure determined?

The assumed value of pressure is usually determined through experimental data or theoretical models. It can also be estimated based on the properties of the material being compressed, such as its elasticity and strength.

## 4. Can the assumed value of pressure change during quasistatic compression?

In most cases, the assumed value of pressure remains constant throughout quasistatic compression. However, it can change if there are significant changes in the material properties or if there are external factors, such as temperature or humidity, that affect the compression process.

## 5. Are there any limitations to using the assumed value of pressure in quasistatic compression?

Yes, there are limitations to using the assumed value of pressure. It is an approximation and may not accurately reflect the actual pressure experienced by the material during compression. It also does not take into account any dynamic or non-quasistatic effects that may occur during compression.

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