What Must Remain Constant for W = pΔV to Apply?

[songoku]

Homework Statement

The work done W by an expanding gas is calculated using W = pΔV. What must remain constant for this equation to be used?
a. The pressure of the expanding gas
b. The pressure of the surroundings
c. The temperature of the expanding gas
d. The temperature of the surroundings
e. (a) and (b) are correct

Homework Equations

W = pΔV

The Attempt at a Solution

My answer is (e). Is it correct?

Thanks

 

[BvU]

Is the presssure of the surroundings in your relevant equation ? If not, where does it come in ?

 

[songoku]

Is the presssure of the surroundings in your relevant equation ? If not, where does it come in ?

"p" in the formula is the pressure of gas.

I think the pressure of surroundings should be constant because I imagine the following case:
Let assume a balloon is heated at constant pressure. The volume of the balloon will increase. If the pressure of the surroundings is not constant, let say increasing, the surroundings pressure will push the balloon so that the volume decreases and it will contradict equation of ideal gas

 

[BvU]

"p" in the formula is the pressure of gas.

I think the pressure of surroundings should be constant because I imagine the following case:
Let assume a balloon is heated at constant pressure. The volume of the balloon will increase. If the pressure of the surroundings is not constant, let say increasing, the surroundings pressure will push the balloon so that the volume decreases and it will contradict equation of ideal gas

In that case the pressure of the gas inside the balloon will also not be constant.

Let me propose another scenario: gas expands at constant pressure pushing a piston in a cylinder. Outside pressure increases but there is also an external force at work that keeps the pressure inside the cylinder exactly constant. Does the gas do work to the tune of $p\Delta V$ or not ?

 

[Chestermiller]

Homework Statement

The work done W by an expanding gas is calculated using W = pΔV. What must remain constant for this equation to be used?
a. The pressure of the expanding gas
b. The pressure of the surroundings
c. The temperature of the expanding gas
d. The temperature of the surroundings
e. (a) and (b) are correct

Homework Equations

W = pΔV

The Attempt at a Solution

My answer is (e). Is it correct?

Thanks

Your answer is correct if, by the pressure of the expanding gas, you mean the force per unit area exerted by the expanding gas at the interface with its surroundings. In a rapid irreversible expansion, the pressure of the expanding gas is not constant spatially within the gas enclosure, and, moreover, there are viscous stresses which contribute to the force per unit area at the interface. But, of course, since the interface has no mass, irrespective of whether the expansion is reversible or irreversible, according to Newton's 3rd law, the force per unit area exerted by the gas at the interface with its surroundings must always match the pressure of the surroundings. So, if that is what you mean by your selection of answer (e), then you are correct.

But, if you are referring to the spatial average pressure of the gas within its enclosure during the expansion, in an irreversible expansion, this would be higher than the force per unit area at the interface where the work is being done. So, in this case, the answer would be (b). I think your professor (or book) is looking for the answer (b) rather than the answer (e).

 

[BvU]

Giving it away, eh ?

 

[Chestermiller]

Giving it away, eh ?

This didn’t seem to me to be something that the OP would be aware of.

 

[conscience]

This didn’t seem to me to be something that the OP would be aware of.

You are absolutely right . Not a single Introductory Physics text discusses this . In fact this is a very common dilemma for someone first studying thermodynamics .

Your first reply is spot on .This question required a nice detailed explanation by an expert .

 

[songoku]

This didn’t seem to me to be something that the OP would be aware of.

Of course I am not aware at all about the thing you explain

I think the answer would be either (a) or (e), never think it would be (b). I will read your post several times to understand it better then I will ask again if I still don't understand about it.Thank you for all the help ( Chestermiller, BvU and conscience)

 

[Chestermiller]

Of course I am not aware at all about the thing you explain

I think the answer would be either (a) or (e), never think it would be (b). I will read your post several times to understand it better then I will ask again if I still don't understand about it.Thank you for all the help ( Chestermiller, BvU and conscience)

Here is an additional link that might help with respect to understanding the correct answer (b): https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/
See just the initial section on the first law of thermodynamics.