first draft 9 23 04 second Sept Oct 2005 minor changes 2006 used spell check expanded example Second Law 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 1 Carnot 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 T H to TL condenser heat rejected from working fluid to T L reservoir infinitesimal T some steam condensed pump temperature raised to T H 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 T H 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 T L reservoir 4 reversible adiabatic process in which the temperature of the working fluid increases from T L to TH Carnot cycle most efficient and only function of temperature efficiency in heat engine thermal W energy sought QH energy that costs QH QL QH 1 QL QH temperature scale arbitrary but defined in terms of Carnot efficiency thermal 1 QL QH TL TH QH QL TH f TL TL f TH proposed by Lord Kelvin thermal 1 TL TH 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 to be 26 80 th 0 2680 1 if want difference to be 100 as on the Celsius scale TH 100 TL 200 initial values 9 25 2006 Given 0 2680 1 TL TH TL T 100 TH TL T TH 2 most efficient TH Find TH TL TL TH 373 134 TL 273 134 T deg C 273 134 T deg K Entropy inequality of Clausius 1 T VW S has 273 15 changed to 273 16 to correspond to triple point of water 0 01 deg C dQ 0 for fig 7 1 1 dQ QH QL 0 from definition of absolute temperature scale and T H and TL constant if 1 T dQ QH TH 1 dQ QL TL 0 approaches 0 TH approaches T L while reversible 1 dQ 0 for all reversible heat engines 1 T T dQ 0 dQ 0 Wirrev Wrev if irreversible with T H TL and QH same QH QL W and 1 QH QL irrev QH QL rev for both 1 dQ QH QL irrev 0 and 1 T dQ QH TH QL irrev QL rev QL irrev TL 0 if heat engine becomes more irreversible such that W 0 as 1 dQ 0 1 T dQ 0 all irreversible engines should do refrigeration cycle as well 9 25 2006 3 1 dQ 0 1 T dQ 0 example 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 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 1 T Saturated vapor 0 7 MPa 2 Boiler dQ 0 90 quality 15 kPa 1 saturated liquid 0 7 MPa heat is transferred in boiler and condenser both at constant T dQ T 1 dQboiler T Condenser 4 Pump 10 quality 15kPa 1 6 mass 1kg on a per unit mass basis kJ h fg 2066 3 q 1 2 h fg q 1 2 2066 3 h f 225 94 x 3 0 9 h 3 h f x 3 h fg x 4 0 …