Projection of P-V-T surface of ideal gas S.J.T.U. Phase Transformation and Applications 不同的温度 ainssald Volume-> Temperature→ 等温线 等容线 不同的体积 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 2 First Law ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 2 First Law II Projection of P-V-T surface of ideal gas 等温线 等容线 不同的温度 不同的体积
Internal energy is only a function of temperature S.J.T.U. Phase Transformation and Applications 温度计 Experiment Joule 1843 低压 四+0-0 气体 真空 A 水浴 简单体系（例子：封闭气体）需由两个变量确定 低压气体的内能仅仅是温度的函数 SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 2 First Law ll
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 2 First Law II Internal energy is only a function of temperature Experiment Joule 1843 δ +δ = UdWQ 简单体系（例子：封闭气体）需由两个变量确定 低压气体的内能仅仅是温度的函数
1.15 Equations of State (2) S.J.T.U. Phase Transformation and Applications Ideal gas:its internal energy does not change with volume at constant temperature. H=U+PV av 〔+ +V aP +业 =0-V+V=0 OH ap OH =0 av ap T SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 2 First Law ll
Phase 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 (2) Ideal gas : its internal energy does not change with volume at constant temperature. ⎟ = 0 ⎠⎞ ⎜⎝⎛ ∂∂V T U ⎟ = ? ⎠⎞ ⎜⎝⎛ ∂∂P T H V P V P P U P H T T T ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ = + VPUH V P RT P P V V U P H T T T ⎟ +⎠⎞ ⎜⎝⎛ ⎟ −+ ⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ 2 ⎟ 0 =+−= 0 ⎠⎞ ⎜⎝⎛ ∂∂ VV PH T ⎟ = ? ⎠⎞ ⎜⎝⎛ ∂∂V T H ⎟ = 0 ⎠⎞ ⎜⎝⎛ ∂∂P T H
1.15 Equations of State (3) S.J.T.U. Phase Transformation and Applications Joule-Thomson coefficient for an ideal gas. aH OT nst T = =0 6H OT )p SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 2 First Law ll
Phase 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 (3) Joule-Thomson coefficient for an ideal gas. ⎟ = 0 ⎠⎞ ⎜⎝⎛ ∂∂P T H = 0 ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ −= ⎠⎞ ⎜⎝⎛ ∂∂ = PT H JT THPH PT η
1.15 Equations of State (4) S.J.T.U. Phase Transformation and Applications Difference in heat capacities of an ideal gas. H=U+PY SJTU Thermodynamics of Materials Spring 2006 X.J.Jin Lecture 2 First Law ll
Phase 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 (4) Difference in heat capacities of an ideal gas. P V VP T U T H CC ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ =− = + VPUH P P T P V P T U T H ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ = ⎠⎞ ⎜⎝⎛ ∂∂ P P V VP T U T V P T U CC ⎟⎠⎞ ⎜⎝⎛ ∂∂ ⎟ − ⎠⎞ ⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ =−