Corrections
p138 Footnote 9 line 5- revised
I wrote ``We could reduce the changing rate by choking the flux instead of reducing the driving force. In this case slowing down the changing rate does not help us to realize reversible change.’’
This applies only when energy loss or gain due to the process is first order in the changing rate.
Therefore, the complete version of this footnote should read:
Why can we generally realize a reversible process by slowing down? Just as the slowly cooling coffee or slow leakage of gas exemplifies, slowing down is not enough to be reversible. However, if the dissipated energy is second or higher order in the rate of change or the driving force of the change, then slowing down can make the total energy dissipation small. For example, suppose the total quantity transported is $Q$ and the dissipation of energy is second order in the changing rate $Q/T$ ($T$ is the total required time). Then the total dissipation is $(Q/T)^2 \times T \propto Q^2/T$, which vanishes in the slow limit $T\map \infty$, even if $Q$ is not small. A good example is Joule heating loss $I^2R$, where $I$ is the current (changing rate of charge) and $R$ is the resistance of the resistor. Thus slowing down by reducing driving forces allows us to realize quasistatic processes.
In contrast, if the energy loss rate is first order in the changing rate $Q/T$, then the total dissipation is $(Q/T) \times T \propto Q$, which does not vanish in the slow limit $T\map \infty$. The two examples at the beginning of this footnote are the examples. Thus, for example, heat flow is reversible only if the flow is between two infinitesimally different temperatures (see 15.6). In this case improving thermal insulation only increases $T$ without changing $Q$, so we must make $Q$ infinitesimal to make the energy loss infinitesimal.
p141 12.13 revised
This item is not accurately stated, because two things are mixed up: the equivalence relation of the thermal equilibrium relation and the existence of the concept of temperature. Thus, the precise statement is:
If systems A and B are in thermal equilibrium, and if B and C are in thermal equilibrium, then so are systems A and C, if in thermal contact. That is, the thermal equilibrium relation is an equivalence relation.
This is often called the zeroth law of thermodynamics.
Then, usually, a demonstration is given of the statement that thermal equilibrium is temperature equilibrium:
there is a scalar quantity called temperature (or more precisely, an empirical temperature) that takes identical values for two systems if and only if they are in thermal equilibrium. [No correction up to this point]
We will not show this (= the existence of temperature), because we do not need this traditional zeroth law to introduce the concept of temperature and because much more assumptions are needed than the zeroth law stating that the thermal equilibrium relation is an equivalence relation.\footnote{See Lenker, T.\ D., (1979).\ Caratheodory's concept of temperature, {\em Synthese}, {\bf 42}, 167-171 (1979).
p179 Jahan A Claes pointed out the error in (15.46) and its explanation just above it. This portion should read
``We should integrate this from 0 to 9N/10 (N/10 remains in the can).’’
and accordingly the integration is from 0 to 9N/10. The answer is correct.
Also he pointed out that I should add some explanation about why there is no entropy change in the bulk gases. I would add:
“The volumes and pressures of the remaining bulk gases change, but the temperatures do not change and the pressure changes are due to reversible mechanical work by the leaking gas, so for the bulk gases as a compound system the net change is adiabatic and reversible; no net entropy changes there. Thus, entropy increase is solely due to this small leakage. ’’
p363 Q28.1 (28.52) The second equality is false. Consequently, the rightmost expression is false. (28.51) is correct.
Careless errors (mentioned in minor errors as well):
p377 One line above 29.2: E = 2PV/3 -> E = 3PV/2.
p386 Footnote 12 (29.37): The overall minus sign is missing from the RHS.