Available Energy - Thermodynamics and Statistical Mechanics - Lecture Slides, Slides of Thermodynamics

Download Available Energy - Thermodynamics and Statistical Mechanics - Lecture Slides and more Slides Thermodynamics in PDF only on Docsity! Thermodynamics and Statistical Mechanics Tds Equations Docsity.com Entropy and Available Energy •Consider two identical bodies, each of mass m, and heat capacity cP, but one at temperature T1, and the other at temperature T2. When placed in contact, heat flows from the hotter to the cooler, until they come to a common temperature, 2 21 TTTf + = Docsity.com “Lost” Work 21 12 2 12 2 121 1 2 2 1 1 2 2 1 1 2 2 10ln 0lnln 0 12 TTT TT T TT T T T T T T dT T dT T dT T dTmc T Qd T Qd f ff ffT T T T P ff ===        =      +      =+       +==+ ∫∫ Run a Carnot engine between the two bodies. Docsity.com Amount of Work [ ] [ ] [ ]     − + = −+= −+= −+−= −= 21 21 2121 21 12 12 2 2 2 2 )()( TTTTmcW TTTTmcW TTTmcW TTTTmcW QQW P P fP ffP Docsity.com Tds Equations dPcdv v cdP P Tcdv v TcTds dPTvdTcdP T vTdTcTds dvTdTcdv T PTdTcTds vP v v P P P P P v v v β κ β β κ β +=      ∂ ∂ +      ∂ ∂ = −=      ∂ ∂ −= +=      ∂ ∂ += Docsity.com First Tds Equation     +      ∂ ∂ =      ∂ ∂ =      ∂ ∂       ∂ ∂ +      ∂ ∂ =     +      ∂ ∂ +=     +      ∂ ∂ += P v u Tv s T c T s dv v sdT T sds dvP v u T dT T cds dvP v udTcTds TT v v Tv T v T v 1 1 Docsity.com First Tds Equation (cont.) vTT v TT v v P v u TTT c v vT s Tv s P v u Tv s T c T s           +      ∂ ∂ ∂ ∂ =      ∂ ∂ ∂∂ ∂ = ∂∂ ∂     +      ∂ ∂ =      ∂ ∂ =      ∂ ∂ 1 1 22 Docsity.com First Tds Equation (cont.)     +      ∂ ∂ =      ∂ ∂     +      ∂ ∂ =      ∂ ∂     +      ∂ ∂ −            ∂ ∂ + ∂∂ ∂ =          +      ∂ ∂ ∂ ∂ ∂∂ ∂ =            ∂ ∂ ∂ ∂ =      ∂ ∂ P v u T PT P v u TT P T P v u TT P vT u T P v u TT Tv u TT u TvT c v Tv Tv TvvT TvT v 2 2 2 2 11 111 11 Docsity.com cP – cv κ β ββ β 2 1 1 Tvcc v P v v T v vTv T PTcc vP v ucc vp T P v vp T vp =−       ∂ ∂−       ∂ ∂ =      ∂ ∂ =−     +      ∂ ∂ =− Docsity.com Ideal Gas P RTP RT vP RT P RT PvP v v T RT R vP R P RT TvT v v TT PP 1 11 1 11 2 = ==      ∂ ∂ −=      ∂ ∂ −= = ==      ∂ ∂ =      ∂ ∂ = κ κ β β Docsity.com Ideal Gas Rcc T PvP T Tvcc Tvcc vp vp vp =− ==− =− 2 2 1 κ β Docsity.com Third Tds Equation dv v TcdP P TcTds dv v T T cdP P T T cds dv v sdP P sds P P v v P P v v Pv       ∂ ∂ +      ∂ ∂ =       ∂ ∂ +      ∂ ∂ =       ∂ ∂ +      ∂ ∂ = Docsity.com Tds Equations dPcdv v cdP P Tcdv v TcTds dPTvdTcdP T vTdTcTds dvTdTcdv T PTdTcTds vP v v P P P P P v v v β κ β β κ β +=      ∂ ∂ +      ∂ ∂ = −=      ∂ ∂ −= +=      ∂ ∂ += Docsity.com