Possible error in book (Thermodynamics: An engineering approach)

In summary: THERMODYNAMICS AN ENGINEERING APPROACH contains a mistake in one of their examples regarding the initial state of a system. The error arises from the definition of the initial state, where the force of the spring is declared to be 0 while the pressure in the cylinder is 200 kPa. This results in a discrepancy in the energy accumulated in the spring and the work done by the gas, which is impossible according to the laws of thermodynamics. The mistake appears to stem from a lack of fundamental understanding and is surprising given the length and reputation of the book. The issue can be resolved by considering the weight of the piston and its gravitational energy, which is not mentioned in the problem statement
  • #1
Juanda
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Hello

I was checking the book THERMODYNAMICS AN ENGINEERING APPROACH (the 2023 version) because I saw it recommended on the internet.

I was surprised to find an error in one of their examples because it is already on the 10th edition. I'm pretty sure about the error but I wanted to confirm it with someone else and maybe contact the writers if necessary and if possible.

I am attaching a picture with the wrong example. It is on page 154, unit 4, example 4-4.
1686487512202.png


The error is born from the definition of the initial state of the system. For context, the pressure of the gas must always be the same as the pressure at the face of the piston (boundary conditions and quasi-equilibrium states). However, in the initial state, it declares the force of the spring is 0 while the pressure in the cylinder is 200 kPa. As a result, later on, they obtain a different number for the energy accumulated in the spring and the work done by the gas which is impossible since all that work will be accumulated as potential energy in the spring.

It is especially surprising to me such an error appears in the book because they are showing the difference in work from the gas and energy in the spring which is not possible so I consider it boils down to a lack of fundamentals. I understand errors are something to be expected with books this long but I would imagine such a mistake would be solved by the 10th edition so I am doubting myself a little.

For the problem to be correct, the force of the spring at the initial state cannot be 0. In fact, its value can be obtained from the provided data and it should be 50kPa (F = P*A). Once doing so, the work done by the gas is the same as the potential elastic energy accumulated by the spring.

Do you also think the book is mistaken?

Do you know how to contact the writers about it?BR
 
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  • #2
Welcome, @Juanda !

It seems to me that the gas could have an initial pressure if the weight of the piston is considered.
The spring then would only add an increasing resistive force to that weight.

Note that the problem states that without the spring, regardless of the amount of thermal energy that is added to the gas, its internal pressure will still be equal to the initial condition.

Also, there are two areas in the graphic representing added work: a rectangular one (moving the mass of the piston up), and a triangular one (moving the piston against the increasing force of the linear spring).
 
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  • #3
Lnewqban said:
Welcome, @Juanda !

It seems to me that the gas could have an initial pressure if the weight of the piston is considered.
The spring then would only add an increasing resistive force to that weight.

Note that the problem states that without the spring, regardless of the amount of thermal energy that is added to the gas, its internal pressure will still be equal to the initial condition.

Also, there are two areas in the graphic representing added work: a rectangular one (moving the mass of the piston up), and a triangular one (moving the piston against the increasing force of the linear spring).

I thought about the weight of the piston as well. However, if that were to be the case, the problem should have mentioned its mass, gravity, or something along those lines. Besides, if the piston has weight, the change in gravitational energy should be considered which isn't in the shown example. I can't understand why would they skip writing information about that weight which will end up absorbing the remaining 10kJ (13kJ done by the gas, 3kJ taken by the spring so 10kJ remaining) as gravitational energy.

Displacement is known (0.2m), energy is known (10kJ) and therefore, the weight must be 5102.04kg (m = E_g/(g*x)→10000/(9.8*.2)). It's a pretty heavy piston but it is what's necessary to make the math work (conservation of energy and quasi-equilibrium states).

Such weight by the way produces the same force in State 1 as the deformed spring I initially proposed (50kN) so that State 1 is in equilibrium. Basically, both alternatives (heavy piston or initially loaded spring) are mathematically equivalent. However, the deformed spring option in State 1 goes against the information provided in the statement. On the other hand, the ghost weight approach doesn't necessarily contradict the information provided although it is necessary to add some considerations that are not mentioned in the problem statement.

My point then stands, would you consider the example in the book incorrect? I find it confusing, to say the least, and downright wrong if you ask me on a bad day. What's your opinion?
 
  • #4
Juanda said:
Hello

I was checking the book THERMODYNAMICS AN ENGINEERING APPROACH (the 2023 version) because I saw it recommended on the internet.

I was surprised to find an error in one of their examples because it is already on the 10th edition. I'm pretty sure about the error but I wanted to confirm it with someone else and maybe contact the writers if necessary and if possible.

I am attaching a picture with the wrong example. It is on page 154, unit 4, example 4-4.
View attachment 327702

The error is born from the definition of the initial state of the system. For context, the pressure of the gas must always be the same as the pressure at the face of the piston (boundary conditions and quasi-equilibrium states). However, in the initial state, it declares the force of the spring is 0 while the pressure in the cylinder is 200 kPa. As a result, later on, they obtain a different number for the energy accumulated in the spring and the work done by the gas which is impossible since all that work will be accumulated as potential energy in the spring.

It is especially surprising to me such an error appears in the book because they are showing the difference in work from the gas and energy in the spring which is not possible so I consider it boils down to a lack of fundamentals. I understand errors are something to be expected with books this long but I would imagine such a mistake would be solved by the 10th edition so I am doubting myself a little.

For the problem to be correct, the force of the spring at the initial state cannot be 0. In fact, its value can be obtained from the provided data and it should be 50kPa (F = P*A) [I meant kN]. Once doing so, the work done by the gas is the same as the potential elastic energy accumulated by the spring.

Do you also think the book is mistaken?

Do you know how to contact the writers about it?BR
Quick note, by the end of the initial message (bold text in this reply) I missed the units at the force done by the spring. I meant 50kN and not kPa. I tried editing the original text but I couldn't manage to do it so I'll write it here.
 
  • #5
Juanda said:
... My point then stands, would you consider the example in the book incorrect? I find it confusing, to say the least, and downright wrong if you ask me on a bad day. What's your opinion?
I hear you.

The numbers seem far from reality:
Weight of 5 tons for a piston of 0.5 meter of diameter, absorbing 5/3 of the work produced by the hot source.
A spring capable of exerting 3 tons of force on 0.2 meter deformation.

These problems tend to specify things to be "weight-less" when they need or want weight to be disregarded.
There is no mention to insulated walls of the cylinder and piston, preventing gas loss of gained heat.
 
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  • #6
Juanda said:
I thought about the weight of the piston as well. However, if that were to be the case, the problem should have mentioned its mass, gravity, or something along those lines. Besides, if the piston has weight, the change in gravitational energy should be considered which isn't in the shown example. I can't understand why would they skip writing information about that weight which will end up absorbing the remaining 10kJ (13kJ done by the gas, 3kJ taken by the spring so 10kJ remaining) as gravitational energy.

Displacement is known (0.2m), energy is known (10kJ) and therefore, the weight must be 5102.04kg (m = E_g/(g*x)→10000/(9.8*.2)). It's a pretty heavy piston but it is what's necessary to make the math work (conservation of energy and quasi-equilibrium states).
You can see from the diagram that the region above the piston is open to the atmosphere. So that contributes a pressure of 100 kPa to the outside face of the piston. So the pressure contributed by the piston is only 100 kPa. For an area of 0.25 m^2, this would represent a force of 25000 N, and a piston mass of about 2500 kg. For a typical steel density of 7700 kg/m^3, this represents a piston volume of 0.32 m^3, and a piston thickness of 1.3 m. It doesn't look like that in the figure. But, if the entire assembly were contained in an outer chamber pressurized to a pressure much closer to 200 kPa, the piston could have a much smaller mass and thickness, and everything could be OK.

I would thus not consider the example in the book as incorrect.
 
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  • #7
Chestermiller said:
You can see from the diagram that the region above the piston is open to the atmosphere. So that contributes a pressure of 100 kPa to the outside face of the piston. So the pressure contributed by the piston is only 100 kPa. For an area of 0.25 m^2, this would represent a force of 25000 N, and a piston mass of about 2500 kg. For a typical steel density of 7700 kg/m^3, this represents a piston volume of 0.32 m^3, and a piston thickness of 1.3 m. It doesn't look like that in the figure. But, if the entire assembly were contained in an outer chamber pressurized to a pressure much closer to 200 kPa, the piston could have a much smaller mass and thickness, and everything could be OK.

I would thus not consider the example in the book as incorrect.
I see what you mean. At this point, I wouldn't exactly say the problem is wrong. It just feels wrong because it is necessary to introduce information that is not considered in the problem to make it work (quasi-equilibrium at State 1 and conservation of energy). I suppose the authors were trying to keep the problem simple and skipped those things that seemed unnecessary to them. However, in my opinion, that only makes it more confusing.

If I were a first-time reader of this I would have taken the example without issues because I wouldn't even have noticed anything. But as someone revisiting these topics when I saw it I had alarms running in my head because something wasn't right. I guess it is up to the readers to decide which approach (skipped details VS all details added) seems more convenient when learning or revisiting the topic.
 
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  • #8
Juanda said:
I see what you mean. At this point, I wouldn't exactly say the problem is wrong. It just feels wrong because it is necessary to introduce information that is not considered in the problem to make it work (quasi-equilibrium at State 1 and conservation of energy).
In the real world, one has to decide on one's own what information is necessary to analyze their system.
Juanda said:
I suppose the authors were trying to keep the problem simple and skipped those things that seemed unnecessary to them. However, in my opinion, that only makes it more confusing.
it may have been a judgment call in editing.
Juanda said:
If I were a first-time reader of this I would have taken the example without issues because I wouldn't even have noticed anything.

Yes, that's what I mean. Adding more detail may have put off the reader.
 
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