Gas Pressure

[Scienc]

Guys, why in this question did the question answer only perform the product between area*P to calculate the mass?

Question:

Answer:

Shouldn't the mass be calculated as m = (P*A)/g?

Considering that:

P = F/A, since: F = m*g

P = (m*g)/A

P*A = (m*g)

m = (P*A)/g

By performing dimensional analysis, you can indeed arrive at the value and unit: 2900 lb. However, I don't understand why gravity wasn't considered.

Edited April 27 by Scienc
I added much space

[sethoflagos]

Your pressure unit is in reality lb force / in² so the result is not lb but lb force. ie. the force exerted in opposition to the gravitational acceleration of a mass of 1 lb at the Earth's surface. 

It's a sloppily presented question: lb / in² is not a correct unit of pressure. g is implicit in both sides of the equation, but cancels.

[Scienc]

Thank you so much.

[Scienc]

8 hours ago, sethoflagos said:

Your pressure unit is in reality lb force / in² so the result is not lb but lb force. ie. the force exerted in opposition to the gravitational acceleration of a mass of 1 lb at the Earth's surface. 

It's a sloppily presented question: lb / in² is not a correct unit of pressure. g is implicit in both sides of the equation, but cancels.

My colleague said that if you know how many square inches there are, you can determine how many pounds are up there based on how many pounds are in each square inch, and it can be obtained by multiplying: area*p

But again, for me, the value obtained is in force unit and not in massa unit.

What am I not understanding?

[exchemist]

17 minutes ago, Scienc said:

My colleague said that if you know how many square inches there are, you can determine how many pounds are up there based on how many pounds are in each square inch, and it can be obtained by multiplying: area*p

But again, for me, the value obtained is in force unit and not in massa unit.

What am I not understanding?

There is a unit of force called “lb force”, which is the force exerted by the weight, at the Earth’s surface, of a mass of 1lb. So lb x g is what it really means.
 

One of the advantages of metric SI units, now used just about everywhere except the USA,  is to avoid the potential confusion of this kind of thing. You would then have mass in kg, force in N and g in m/sec squared and less risk of confusing mass with force.

 

Edited April 27 by exchemist

[Scienc]

14 minutes ago, exchemist said:

There is a unit of force called “lb force”, which is the force exerted by the weight, at the Earth’s surface, a mass of 1lb. So lb x g is what it really means.
 

One of the advantages of metric SI units, now used just about everywhere except the USA,  is to avoid the potential confusion of this kind of thing. You would then have mass in kg, force in N and g in m/sec squared and no scope to confuse mass with force.

 

Thanks.

Edited April 27 by Scienc

[exchemist]

20 minutes ago, Scienc said:

Does this mean I'm right? And the correct value for the mass of the gas is lbf*g, which means the value 2900 needs to be multiplied by 9.8?

You are muddling metric and old-fashioned Imperial units.  g in old units is 32ft/sec squared. g is 9.8 m/sec squared in  modern SI units.
 

If you multiply lb by g in old units you get the force in something called poundals, defined as the force needed to give a 1lb mass an acceleration of 1ft/sec squared. So there are 32 poundals in 1 lb-force. A pressure given in units of lb/sq in is implicitly in units of lb-force, not lb mass. lb-force is a force unit already, so no need to multiply by g.  

It’s a nightmare.  If you really want to do your head in, read this: https://en.wikipedia.org/wiki/Poundal

 

 

Edited April 27 by exchemist

[Scienc]

2 minutes ago, exchemist said:

No because you are muddling metric and old-fashioned Imperial units.  g in old units is 32ft/sec squared. g is 9.8 m/sec squared in  modern SI units.
 

If you multiply lb by g in old units you get the force in something called poundals, defined as the force needed to a 1lb mass an acceleration of 1ft/sec squared. So there are 32 poundals in 1 lb-force. A pressure given in units of lb/sq in is implicitly in units of lb-force, not lb mass. lb-force is a force unit already, so no need to multiply by g.  

It’s a nightmare.  If you really want to do your head in, read this: https://en.wikipedia.org/wiki/Poundal

 

 

I realized that the mistake I made was a technical one, and not related to the issue at hand. My assumption of using Newton's second law would only make sense if the pressure unit was in Pa or N/m^2. 

 

However, since the pressure value was given in lbf/in2, the value obtained by multiplying the area with P (in lbf/in2) is numerically equal to the mass value. 

 

The response was a bit unclear, but it should have been understandable. As you pointed out, the weight of one pound is equivalent to one lbf here on earth. Therefore, if they wanted to clarify this, they could have done a conversion using the conversion factor of 1. However, this conversion should be understood even if it is not explicitly mentioned.

[exchemist]

5 minutes ago, Scienc said:

I realized that the mistake I made was a technical one, and not related to the issue at hand. My assumption of using Newton's second law would only make sense if the pressure unit was in Pa or N/m^2. 

 

However, since the pressure value was given in lbf/in2, the value obtained by multiplying the area with P (in lbf/in2) is numerically equal to the mass value. 

 

The response was a bit unclear, but it should have been understandable. As you pointed out, the weight of one pound is equivalent to one lbf here on earth. Therefore, if they wanted to clarify this, they could have done a conversion using the conversion factor of 1. However, this conversion should be understood even if it is not explicitly mentioned.

Yes I think you have got it. I admit I don’t know how this is presented to students in the US today. My experience with Imperial units dates from schooldays in the UK in the early 1970s, when we transitioned from Imperial to metric. I remember how awful it was, compared to the simplicity of metric, and specifically, the version of metric that later came to be known as Systeme International (SI) units. 

[sethoflagos]

3 hours ago, Scienc said:

However, since the pressure value was given in lbf/in2, the value obtained by multiplying the area with P (in lbf/in2) is numerically equal to the mass value. 

Understand this and you clear the confusion.

F = ma

Weight = Mass x gravitational acceleration

lb force = lb mass x g/32.2

ie if we equate weight numerically with mass, we're implicitly adopting some unit of acceleration that has the numerical value of 1 at the earth's surface. As @exchemist has pointed out, this creates a great deal of needless complications in US technical literature. Many equations end up littered with this dimensional constant of 32.2 simply to maintain this unity factor between weight and mass. Either that or adopt that most wonderfully named of all units, the slug foot.

See https://en.wikipedia.org/wiki/Gc_(engineering)

4 hours ago, Scienc said:

My colleague said that if you know how many square inches there are, you can determine how many pounds are up there based on how many pounds are in each square inch, and it can be obtained by multiplying: area*p

Only approximately. The higher levels of the earth's atmosphere are subject to a lower gravitational acceleration due to their increased distance from the centre of mass so they weigh less per unit mass. This illustrates quite nicely how careless application of the unity assumption can simply lead to incorrect results.

Edited April 27 by sethoflagos
sp

[Prajna]

On 4/27/2024 at 2:03 PM, exchemist said:

If you multiply lb by g in old units you get the force in something called poundals, defined as the force needed to give a 1lb mass an acceleration of 1ft/sec squared. So there are 32 poundals in 1 lb-force.

A poundal is the certain force -

or so my dictionary reckoned -

to accelerate a pound of weight

by one foot per second per second.

(written some years ago)

[exchemist]

4 hours ago, Prajna said:

A poundal is the certain force -

or so my dictionary reckoned -

to accelerate a pound of weight

by one foot per second per second.

(written some years ago)

Which is what I said.

[Prajna]

3 hours ago, exchemist said:

Which is what I said.

Almost verbatim.