エンタルピーの計算 dH = T ∂P ∂T ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ dV + CV T dT
itlrouY;7 /%XEitlroug P-‐V-‐T ?Hc+_dB/%(4"g1DS;7OdX >Y:DbEXxH = f (V, T) UOdB/%(4"YKIxP = f (V, T) Y?'#gdMUID YTB ⎫ ⎧⎛ ∂P ⎞ C ⎛ ∂P ⎞ dH = T ⎨⎜ dV + V dT ⎬ + VdP = T ⎜ dV + CV dT + VdP ⎟ ⎝ ∂T ⎟⎠ V T ⎩⎝ ∂T ⎠ V ⎭ P-‐V-‐T ?Y.XGDSZx-! T gUNSxgFQYqr5g+ _dvDfadx6-8g+_dwBT yUOdUx ⎫ ⎧⎛ ∂P ⎞ CV ⎛ ∂P ⎞ dH = T ⎨⎜ dT ⎬ + VdP = T ⎜ dV + VdP ⎟⎠ dV + ⎝ ⎝ ∂T ⎟⎠ V T ⎩ ∂T V ⎭ *YXZxPV = ZRT TCdHcxVdP = −PdV + RTdZ NQIRSx ⎧ ⎛ ∂P ⎞ ⎫ dH = − ⎨ P − T ⎜ dV + RTdZ ⎝ ∂T ⎟⎠ V ⎬⎭ ⎩ R ⎛ ∂P ⎞ = , Z =1 ⎝ ∂T ⎟⎠ V V 0$*Yg@dH* UOe[x⎜ TCdHcx dH ∗ = 0 "Y gRSx0$*Y/% (V = ∞)@Hcx*Y/% (V = V) ]T5OdU Vm ⎡ ⎛ ∂P ⎞ ⎤ H m∗ − H m = ∫ ⎢ P − T ⎜ ⎟⎠ ⎥ dVm − RT ( Z − 1) ∞ ⎝ ∂T Vm ⎦ ⎣ <YMUgitlrou U\BMY<Y5YXxF[@vdW/%(4"W Vge=^MUTx32,YitlrouI;7T+_cedYTCdB itnsouY;7 U)XNSx/%XEitnsoug P-‐V-‐T ?Hc+_dB C ⎛ ∂P ⎞ dS = ⎜ dV + V dT ⎝ ∂T ⎟⎠ V T ⎡ ⎤ ⎛ ∂P ⎞ ∴ ⎢ dS = ⎜ dV ⎥ ⎟ ⎝ ∂T ⎠ V ⎣ ⎦T 0$*Yg@dS* UOe[x R ⎛ ∂P ⎞ dS ∗ = ⎜ dV = dVm ⎟ ⎝ ∂T ⎠ V Vm "Y gRSx0$*Y/% (V = ∞)@Hcx*Y/% (V = V) ]T5OdU Vm ⎡ R ⎛ ∂P ⎞ ⎤ Sm∗ − Sm = ∫ ⎢ − ⎜ ⎟⎠ ⎥ dVm ∞ ⎝ V ∂T Vm ⎦ m ⎣ pjkmhu'Y;7 ln φ = ln f 1 = P RT ∫ (V P m 0 − Vm∗ ) dP MY`x;7X/%(4"g1DdMUg9FSx5'g V X&OdB PVm = ZRT TCdHcxdP = − *YXZx ln φ = ln f 1 = P RT ∫ (V P 0 m − Vm∗ ) dP = 1 RT ∫ P 0 P RT dVm + dZ NQIRSx Vm Vm ⎡ P RT ⎞ ⎤ ∗ ⎛ dZ ⎟ ⎥ ⎢(Vm − Vm ) ⎜ − dVm + Vm ⎝ Vm ⎠⎦ ⎣ P : 0 → P YUJXxVm : ∞ → Vm, Z : 1 → Z TCdHcx 1 RT 1 RT ∫ Z 1 ∫ Vm ∞ ⎡ 1 P ⎞⎤ ∗ ⎛ ⎢(Vm − Vm ) ⎜ − ⎟ ⎥ dVm = RT ⎝ Vm ⎠ ⎦ ⎣ (Vm − Vm∗ ) ∴ln φ = ln ∫ Vm ∞ ⎡ PVm∗ ⎤ 1 ⎢ V ∗ − P ⎥ dVm = RT ⎣ ⎦ ∫ Vm ∞ ⎡ RT ⎤ ⎢⎣ V ∗ − P ⎥⎦ dVm Z⎛ Z⎛ Z⎛ RT V∗ ⎞ RT P ⎞ 1⎞ dZ = ∫ ⎜ 1− m ⎟ dZ = ∫ ⎜ 1− dZ = ∫ ⎜ 1− ⎟ dZ = Z − 1− ln Z ⎟ 1 ⎝ 1 ⎝ 1 ⎝ Vm Vm ⎠ ZRT P ⎠ Z⎠ f 1 = P RT ∫ (V P 0 m − Vm∗ ) dP = 1 RT ∫ Vm ∞ ⎡ RT ⎤ ⎢⎣ V ∗ − P ⎥⎦ dVm + Z − 1− ln Z A/%(4"UNSxSRKA"g1DSxpjkmhu'Y;7"gPbB A-! 473.15 K, 10 MPa XGLd N2, H2, NH3 Ypjkmhu'g SRK "g1DS;7PbB TC [ K ] PC [ MPa ] ω N2 126.2 3.39 0.039 H2 33.0 1.29 -‐0.216 NH3 405.5 11.35 0.250
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