relaxation time) the work done in reaching the equilibrium point (the first time) may he calculated as J P...dV . The equations here give a more quantitative picture of what is required in determining 'Lsmallness." Because t,hework can differfrom the reversible value, there exists a mechanism for slow dissipation of the oscillational energy of the piston about the equilibrium point. Any "excess work" done on the gas must appear as an increase in kinetic energy of the gas; indeed, all work done on the gas appears as an increase in the kinetic energy of the gas molecules. This is the meaning of the work-energy theorem for a particle and of the first-law equation. It is not correct to call this increased thermal energy "heat," however, unless it is transferred as heat. If we require that the ideal gas be isothermal the energy of the gas will he constant. The work done on the gas molecules by the piston is transferred as heat from the gas to the surroundings. ROBERTBAUMAN
To the Editor: What is the normal melting point of carbon dioxide? No matter what additional data are provided and how good one's background in thermodynamics, statistical mechanics, and quantum theory, there can be no correct answer to this problem. Carbon dioxide just does not have a normal melting point, any more than there is a definite date on which the good husband stopped beating his wife. But whereas here the situation is simple, there are more subtle forms of this type of problem which may be very confusing. Professor Bauman seems to have pinpointed a common type while analyzing the problem of compressing isothermally a gas originally a t 1 atm by a constant external pressure of 5 atm. It seems clear (although only after study of the arguments raised by his article) that there can be no correct answer to the
problem as stated, because there is no way of applying a 5 atm pressure directly to a gas a t 1 atm without involving inertial effects due to acceleration of the gas which prevents isothermal performance of the p r e scribed process. This direct contact between a gas a t high and one a t low pressure is used in shock tubes to obtain transient high temperatures. I n order to overcome this impossibility of the verbatim interpretation of the problem, one instinctively introduces some additional assumption such as the one that there exists a piston confining the gas and that the pressure is applied to the piston. This permits the inertia. of the piston to take up the unbalance of the pressures on its two sides. Then if one emphasizes the part of the question which asks about the work done "by the gas" and considers the piston as part of surroundings, one can follow Professor Bauman's solution. However if one neglects this and concentrates on the applied external pressure, considering the piston as part of the system, one can follow Professor Chessick. I n either case, however, there is the difficulty of the energy stored in the moving piston. Again the tacit assumption has been made above that this energy is somehow dissipated and that the piston does come to a rest. I n fact however, as Professor Bauman emphasizes, if the system is isothermal and frictionless, i.e. reversible, this will not happen. The system does not come to rest so that again no answer can be given. As pointed out in the original article, if the mechanism by which the piston dissipates its energy is considered in detail, various correct answers can be obtamed. I n conclusion, we can he grateful to Professor Bauman for having clarified our thmking on a familiar, but really not simple, model process. Perhaps, however, he also was too rash in providing a "correct" answer to a problem which does not have one.
P.S. h ' t it true, however, that from a student's point of view the correct answer is simply the one that the professor expects? This in turn can be antioipated from the professor's teaching.
Volume 41, Number 12, December 1964
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