1.15 Equations of State(5) S.J.T.U. Phase Transformation and Applications U=U(T,V) V=V(T,P) dy= 器 dT+P ) dy +器 du= ）an At constant pressure dP=0 -em.+[em】 D SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 2 First Law llPhase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 2 First Law II 1.15 Equations of State (5) = VTUU ),( Vd V U PdT T U Ud V T ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = = PTVV ),( dP P V PdT T V Vd P T ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = ⎥⎦⎤ ⎢⎣⎡ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = dP PV dT TV VU PdT TU Ud V T P T At constant pressure dP=0 ( ) ( ) ( ) ⎥⎦⎤ ⎢⎣⎡ ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = P T P P V P dT TV VU dT TU Ud T P U ⎟⎠⎞ ⎜⎝⎛ ∂∂