ee 22 23 2 Hence F(71,Ty)=F(T,T2)×F(T2,r) Not a function Cannot be a function of 72 We thus conclude that F(T, T)has the form f(T)/f(T2),and similarly F(T,T)=f(T)/f(T). The ratio of the heat exchanged is therefore g-n(,)- f(T3 In general OH f(TH er f( so that the ratio of the heat exchanged is a function of the temperature. We could choose any function that is monotonic, and one choice is the simplest: f(T)=T. This is the thermodynamic scale of temperature, QH/Q=TH/T. The temperature defined in this manner is the same as that for the ideal gas; the thermodynamic temperature scale and the ideal gas scale are equivalent 1. C3 Representation of Thermodynamic Processes in T-s coordinates. It is often useful to plot the thermodynamic state transitions and the cycles in terms of temperature(or enthalpy)and entropy, T, S, rather than P, The maximum temperature is often the constraint on the process and the enthalpy changes show the work done or heat received directly, so that plotting in terms of these variables provides insight into the process. A Carnot cycle is shown below in these coordinates, in which it is a rectangle, with two horizontal, constant temperature legs. The other two legs are reversible and adiabatic, hence isentropic (ds= dQ /T=0), and therefore vertical in T-s coordinates Isothermal Adiabatic 几L Carnot cycle in T,s coordinates If the cycle is traversed clockwise, the heat added is 1C-41C-4 Q Q Q Q Q Q 1 3 1 2 2 3 = . Hence FT T FT T FT T T T 1 3 2 12 23 2 ( ) , ,, = ( ) × ( ) Not a function of Cannot be a function of 1 24 341 2 444 3 444 . We thus conclude that FT T1 2 ( ) , has the form fT fT () () 1 2 / , and similarly FT T f T f T 23 2 3 ( ) , / = ( ) ( ). The ratio of the heat exchanged is therefore Q Q FT T f T f T 1 3 1 3 1 3 = ( ) = ( ) ( ) , . In general, Q Q f T f T H L H L = ( ) ( ) , so that the ratio of the heat exchanged is a function of the temperature. We could choose any function that is monotonic, and one choice is the simplest: fT T ( ) = . This is the thermodynamic scale of temperature, QQ TT H L HL = . The temperature defined in this manner is the same as that for the ideal gas; the thermodynamic temperature scale and the ideal gas scale are equivalent 1.C.3 Representation of Thermodynamic Processes in T-s coordinates. It is often useful to plot the thermodynamic state transitions and the cycles in terms of temperature (or enthalpy) and entropy, T,S, rather than P,V. The maximum temperature is often the constraint on the process and the enthalpy changes show the work done or heat received directly, so that plotting in terms of these variables provides insight into the process. A Carnot cycle is shown below in these coordinates, in which it is a rectangle, with two horizontal, constant temperature legs. The other two legs are reversible and adiabatic, hence isentropic ( dS dQ T = rev / = 0), and therefore vertical in T-s coordinates. T TH TL Isothermal Adiabatic s Carnot cycle in T,s coordinates If the cycle is traversed clockwise, the heat added is a c b d