Second Law first draft 9/23/04, second Sept Oct 2005 minor changes 2006, used spell check, expanded example Kelvin-Planck: It is impossible to construct a device that will operate in a cycle and produce no effect other than the raising of a weight and the exchange of heat with a single reservoir. Clausius: It is impossible to construct a device that operates in a cycle and produces no other effect than the transfer of heat from a cooler body to a hotter body. Woud: used to: 1) predict the direction of processes 2) establish the conditions of final equilibrium 3) determine best possible theoretical performance of a process if it is impossible to have a heat engine with 100% efficiency, how high can it go?? define ideal process, termed reversible process: a process that, once having taken place, can be reversed without changing either the system or surroundings examples irreversible; piston expanding against stop reversible; piston expanding by removing and replacing weights; excerpt from VW&S page 166 good description of reversible and irreversible processes Let us illustrate the significance of this definition for a gas contained in a cylinder that is fitted with a piston. Consider first Fig. 6.8, in which a gas (which we define as the system) at high pressure is restrained by a piston that is secured by a pin. When the pin is removed, the piston is raised and forced abruptly against the stops. Some work is done by the system, since the piston has been raised a certain amount. Suppose we wish to restore the system to its initial state. One way of doing this would be to exert a force on the piston, thus compressing the gas until the pin could again be inserted in the piston. Since the pressure on the face of the piston is greater on the return stroke than on the initial stroke, the work done on the gas in this reverse process is greater than the work done by the gas in the initial process. An amount of heat must be transferred from the gas during the reverse stroke in order that the system have the same internal energy it had originally. Thus the system is restored to its initial state, but the surroundings have changed by virtue of the fact that work was required to force the piston down and heat was transferred to the surroundings. Thus the initial process is an irreversible one because it could not be reversed without leaving a change in the surroundings. In Fig. 6.9 let the gas in the cylinder comprise the system and let the piston be loaded with a number of weights. Let the weights be slid off horizontally one at a time, allowing the gas to expand and do work in raising the weights that remain on the piston. As. the size of the weights is made smaller and their number is increased, we approach a process that can be reversed, for at each level of the piston during the reverse process there will be a small weight that is exactly at the level of the platform and thus can be placed on the platform without requiring work. In the limit, therefore, as the weights become very small, the reverse process can be accomplished in such a manner that both the system and surroundings are in exactly the same state they were initially. Such a process is a reversible process. 9/25/2006 1Carnot cycle example steam power plant - working substance steam boiler - heat transferred from high T (constant) reservoir to steam - steam T only infinitesimally lower than reservoir => reversible isothermal heat transfer process. (phase change fluid - vapor is such a process turbine - reversible adiabatic (no heat transfer) T decreases from TH to TL condenser - heat rejected from working fluid to TL reservoir (infinitesimal ΔT) some steam condensed pump - temperature raised to TH adiabaticly can reverse and act as refrigerator Carnot cycle four basic processes: 1. reversible isothermal process in which heat is transferred to or from the TH reservoir 2. reversible adiabatic process in which the temperature of the working fluid decreases from T H to TL 3. reversible isothermal process in which heat is transferred to or from the TL reservoir 4. reversible adiabatic process in which the temperature of the working fluid increases from TL to TH Carnot cycle most efficient, and only function of temperature efficiency (in heat engine) W = energy_sought QH − QL QL ηthermal = QH = energy_that_costs = QH = 1 − QH temperature scale (arbitrary but defined in terms of Carnot efficiency) fTH ηthermal = 1 − QL = ψ(TL, TH) QH = ( ) = TH proposed by TL QH QL ( TL Lord Kelvin ηthermal = 1 − TH most efficientfTL) at this point have ratio of absolute temperatures derive scale from non-Carnot heat engine operating at steam T H and ice temperature TL if we could measure it would find η TH to be 26.80% ηth = 0.2680 = 1 − TL if want difference to be 100 as on the Celsius scale ΔT := 100 TH := 100 TL := 200 Given TL initial values 0.2680 = 1 − TH = TL + ΔT TH 9/25/2006 2⎛⎜ ⎜⎝ ⎞⎟ ⎟⎠ :=) ⎛⎜ ⎜⎝ TH TL ⎛⎜⎝ ⎞⎟ ⎟⎠ 373.134 273.134 ⎞⎟⎠ = TH Find TH TLTL T_deg_C + 273.134 = T_deg_K VW&S has 273.15 changed to 273.16 to correspond to triple point of water 0.01 deg_C ,(Entropy inequality of Clausius ... ⌠⎮ ⎮⌡ 1 dQ ≤ 0 T for fig 7.1 ⌠⎮⌡ 1 dQ QH− QL > 0= from definition of absolute temperature scale and TH and TL constant ⌠⎮ ⎮⌡ QH− QL1 Q = 0d = T TH TL ⌠⎮ ⎮⌡ 1 dQ = 0 T ⌠⎮⌡ if .. 1 dQ approaches 0, TH approaches TL, while reversible ⌠⎮ ⎮⌡ ⌠⎮⌡ 1 dQ ≥ 0 and ... 1 dQ = 0 T=> for all reversible heat engines ... if irreversible, with TH, TL, and QH same ... Wirrev Wrev< for bothQH− QL = W QH− QL_irrev QH− QL_rev => QL_irrev QL_rev< > ⌠⎮⌡ and ...1 dQ QH− QL_irrev > 0= ⌠⎮ ⎮⌡ QH−QL_irrev1 dQ < 0= T TH TL if heat engine becomes more irreversible such that W => 0.. as ... ⌠⎮⌡ 1 dQ = 0 ⌠⎮ ⎮⌡ 1 T dQ < 0 => all irreversible engines ⌠⎮ ⎮⌡ ⌠⎮⌡ 11 dQ ≥ 0 dQ < 0 T should do refrigeration cycle as well 9/25/2006 3example figure 7.3 pg 188 VW&S example fig 7.3 - simple steam power plant cycle - not typical - pump handles mixture of liquid and vapor in such Saturated vapor, 0.7 MPa proportions that saturated liquid leaves the pump and enters the boiler. The pressures and quality at various points are given in the figure. ? Does this data satisfy the inequality of Clausius? ⌠ inequality of Clausius ... ⎮⎮ T1 dQ ≤ 0 ⌡ heat is transferred in boiler and condenser, both at