Thermodynamics reference books

[khil_phys]

Hi,

I am a grade 11 student preparing for the IIT-JEE. I would like to know about some good books on thermodynamics. Young, Sears Zemansky & Resnick/Halliday/Walker don't go into much depth on this topic.

 

[Philip Wood]

Both Sears and (separately) Zemansky produced single-subject Thermodynamics books. Zemansky, though written some fifty years ago, is in my opinion, very careful and thorough - first rate. A later edition came out under the joint names of Zemasnsky and Dittman. As far as I could tell, the main change was the addition of a chapter on statistical mechanics (which didn't really improve the book). Sears, I know little about.

Both these books are essentially about classical thermodynamics: what can be deduced about systems from applying the three or four Laws of Thermodynamics to systems about which we assume very little microscopic knowledge.

Classical thermodynamics is a remarkably beautiful subject, but needs time to absorb and appreciate. Partly – but not wholly – to save teaching time there is a modern approach which tries to integrate classical thermodynamics, and the more microscopically-based, and further-reaching, statistical mechanics. In my opinion one of the best texts of this type is Statistical Physics by Franz Mandl. Its develops the ideas cleanly without getting bogged down in difficult details. Fundamentals of Statistical and Thermal Physics by Reif attempts the same integrated approach but is much longer (and, in my opinion, does no better a job than Mandl).

 

[khil_phys]

Thanks a lot! Will surely look follow your guidance.

 

[Philip Wood]

I should have mentioned another introductory textbook: Equilibrium Thermodynamics by Adkins, now in its third edition. It's another 'pure' thermodynamics book, that is it doesn't try to integrate thermodynamics and statistical mechanics. I'm not as familiar with it as I am with Zemansky, but I have skimmed it and it looks to be an excellent treatment: more concise than Z, but giving very clear explanations. See the reviews on a well known mail-order site.

 

[khil_phys]

The main problem that I was having was in the conduction portion and its equations. My school text doesn't explain much, leaving it just to be crammed, which is unacceptable to me.

 

[khil_phys]

Both these books are essentially about classical thermodynamics: what can be deduced about systems from applying the three or four Laws of Thermodynamics to systems about which we assume very little microscopic knowledge.

Classical thermodynamics is a remarkably beautiful subject, but needs time to absorb and appreciate.

By the way, HRW does have a section on thermal physics. Will it be sufficient for the high school level? Or will I have to get one of the ones you mentioned above.

 

[Philip Wood]

I'm sorry not to have got back to you on textbooks covering thermal conductivity. None of the books I mentioned says a great deal about it, and I don't really know how deep you need to go. This isn't helped by my being English, so I don't know what a high school course would cover. If it's like A-Level in the UK, you wouldn't have to know much more than the one-dimensional defining equation for thermal conductivity:
$$\frac{dQ}{dt} = -\kappa A \frac {dT}{dx},$$
and how to apply it in steady-state situations.
More advanced work would include three dimensional heat flow, and non-steady-state situations, as well as microscopic treatments of thermal conduction in gases. None of the books I've mentioned seems to cover all these cases - but my guess is that you may not need to consider them just yet.

 

[khil_phys]

Well, that clears it up a lot. I should have let you know what exactly I want to know regarding thermal conduction.

The topics in my text include the equation you mentioned and it's applications in steady-state conditions and, additionally, thermal resistance. I'm actually looking for texts that cover these topics, though I must let you know that anything more than that will do absolutely no harm.

That means that I will definitely have to go for undergrad level texts, or even higher, if the situation so demands.

 

[khil_phys]

So, I need texts which cover both thermal resistance and conductance, and maybe more than that.

 

[Philip Wood]

There's not really much to know about thermal resistance and conductance. Are you familiar with the equation for current I flowing through a conductor of length L and cross-sectional area A, namely:
$$I = \frac{\sigma A}{L} V ?$$
V is the p.d. between the ends of the wire, and $$\sigma$$ is the electrical conductivity of the material.

Do you see that there's an exact correspondence between the thermal and electrical conduction equations? dQ/dt is rate of flow of heat; I is rate of flow of charge. dT/dx is temperature gradient; V/L is potential gradient. A means cross-section in both cases.

Now, in the electrical case, (sigma A)/L is called the electrical conductance of the conductor, so, in the thermal case, (kappa A)/delta x is called the thermal conductance of the bar or slice.

The reciprocals of the thermal and electrical conductances are called the thermal and electrical resistances. 1/kappa would be the thermal resistivity (though this term isn't used much). 1/sigma is called rho, the electrical resistivity.

One of the useful things about the analogy is that you can now handle problems about thermal conduction in bars or slices in series and in parallel, just as though they were electrical resistances. But you can only do this if they're in their steady state ( temperature no longer changing at any point), and heat leakages through the sides are negligible.

 

[khil_phys]

So, the equation of heat current is analogous to that of electric current. But, my question here is that whoever formulated it must have derived it in some way. By comparing it with electric current could be a way of simple explanation.

But, on the whole, I believe you're trying to say that thermal resistance and conductance are not so important in thermodynamics as are the three laws.

 

[Philip Wood]

But, on the whole, I believe you're trying to say that thermal resistance and conductance are not so important in thermodynamics as are the three laws.

I wasn't trying to say this, but it is something I might have said! The thermal conductivity equation deals with heat flow, which is a small part of thermal Physics. But the Zeroth, first and second law of thermodynamics are applicable to all systems.
[That doesn't mean that you should learn these laws now. The second law, for example, is usually regarded as a university topic. You need to get a feeling for thermal Physics before tackling it.]

So, the equation of heat current is analogous to that of electric current. But, my question here is that whoever formulated it must have derived it in some way. By comparing it with electric current could be a way of simple explanation.

It is possible to derive the heat flow equation, by studying what's happening on the level of particles (atoms or molecules), but that's university work, though a dumbed-down, hand-waving treatment is possible. At an introductory level, I'd regard it as an experimental equation - it is supported by experiment.

The treatment I gave in my previous post, drawing the analogy between thermal and electrical conduction, is a standard introductory treatment. Let me know if you don't follow it.

A general pedagogic point here... You clearly have a desire to get to the bottom of things, and don't want to be fobbed off with analogies and plausibility arguments. But I'd urge patience: in thermal Physics especially, you really do need a good feel for the simple stuff, heat flow, thermal capacity, work done on a gas, internal energy and so on, before going for the intellectual high ground, such as the second law of thermodynamics.

 

[khil_phys]

But I'd urge patience: in thermal Physics especially, you really do need a good feel for the simple stuff, heat flow, thermal capacity, work done on a gas, internal energy and so on, before going for the intellectual high ground, such as the second law of thermodynamics.

So, although it is true for every field of physics, thermal physics has to be learned in the correct order.

As an example, I might say that my question regarding the derivation of the equation of thermal resistance will get an answer just at the right time. I cannot skip a whole lot for that.

 

[Philip Wood]

Good. I thought you might like to test your understanding of the thermal conductivity equation and related ideas with a straightforward question. [Note: if you've been taught to measure heat in calories rather than joules, you can convert the data using 1 cal = 4.18 J, so 1 J = 0.239 cal, 1 W = 0.239 cal s^-1, but it's easier here to stick to SI units, that is joules and watts.]

A bar of copper has a length of 0.10 m and a cross-sectional area of 12.0 x 10^-4 m². The thermal conductivity of copper is 400 W m^-1 K^-1. The sides of the bar are 'lagged' with wool to prevent heat flow out of (or into) the sides.

(a) Check that you understand why the (SI) units of thermal conductivity are W m^-1 K^-1.

(b) Calculate the rate of flow of heat through the bar in the steady state when one end is kept at 20°C and the other end at 100°C. [380 W (2 sigfigs) = 92 cal s^-1]

(c) Calculate the thermal resistance of the bar. [0.208 K W^-1]

(d) Calculate the thermal resistance of a lagged aluminium bar of the same size and shape, given that the thermal conductivity of aluminium is 250 W m^-1 K^-1. [0.333 K W^-1]

(e) If the two bars are placed in good contact, end-to-end, to make one bar 0.24 m long, calculate the thermal resistance of the composite bar. [0.54 K W^-1]

(f) Calculate the heat flow rate of flow of heat through the composite bar in the steady state when one end is kept at 20°C and the other end at 100°C. [148 W]