Editing Content :: Admin Scraper

Chapter

Content type

Position

Value

THERMODYNAMICS 239 To prove the result (a), imagine a reversible reservoir and delivers the same amount of work (Carnot) engine R and an irreversible engine I in one cycle, without any change in the source working between the same source (hot reservoir) or anywhere else. This is clearly against the and sink (cold reservoir). Let us couple the Kelvin-Planck statement of the Second Law of engines, I and R, in such a way so that I acts Thermodynamics. Hence the assertion η > η I R like a heat engine and R acts as a refrigerator. is wrong. No engine can have efficiency greater Let I absorb heat Q f1om the source, deliver than that of the Carnot engine. A similar work W ′ and release the heat Q - W ′ to the sink. argument can be constructed to show that a 1 We arrange so that R returns the same heat Q 1 reversible engine with one particular substance to the source, taking heat Q 2rom the sink and cannot be more efficient than the one using requiring work W = Q – Q to be done on it. another substance. The maximum efficiency of 1 2 Now suppose η R < ηI i.e. if R were to act a Carnot engine given by Eq. (11.27) is as an engine it would give less work output independent of the nature of the system performing the Carnot cycle of operations. Thus we are justified in using an ideal gas as a system in the calculation of efficiency η of a Carnot engine. The ideal gas has a simple equation of I state, which allows us to readily calculate η, but the final result for η, [Eq. (11.27)], is true for any Carnot engine. R This final remark shows that in a Carnot cycle, Q1 = T1 W Q2 T2 (11.28) Fig. 11.10 An irreversible engine (I) coupled to a is a universal relation independent of the nature of the system. Here Q and Q are respectively, reversible refrigerator (R).′> W, this 1 2 would amount to extraction of heat the heat absorbed and released isothermally W ′– W from the sink and its full (from the hot and to the cold reservoirs) in a conversion to work, in contradiction withCarnot engine. Equation (11.28), can, therefore, the Second Law of Thermodynamics. be used as a relation to define a truly universal thermodynamic temperature scale that is than that of I i.e. W < W′ for a given Q . With R independent of any particular properties of the 1 acting like a refrigerator, this would mean system used in the Carnot cycle. Of course, for Q 2 Q – 1 > Q – W ′1 Thus, on the whole, an ideal gas as a working substance, this the coupled I-R system extracts heat universal temperature is the same as the ideal (Q1– W) – (Q –1W ′) = (W ′ – W ) from the cold gas temperature introduced in section 11.9. SUMMARY 1. The zeroth law of thermodynamics states that ‘two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other’. The Zeroth Law leads to the concept of temperature. 2. Internal energy of a system is the sum of kinetic energies and potential energies of the molecular constituents of the system. It does not include the over-all kinetic energy of the system. Heat and work are two modes of energy transfer to the system. Heat is the energy transfer arising due to temperature difference between the system and the surroundings. Work is energy transfer brought about by other means, such as moving the piston of a cylinder containing the gas, by raising or lowering some weight connected to it. Reprint 2026-27