6.27 - 6 6.27 (a) dU = TdS PdV + GdN FG U IJ = P ; H V K FG...

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6.27 (a) dU TdS PdV GdN U S T VN =− + ⇒ F H G I K J = , ; U V P SN F H G I K J =− , ; and U N G SV F H G I K J = , Now equating mixed second derivatives V U SS U V T V P S V N ,,,, , , F H G I K J = F H G I K J F H G I K J F H G I K J (1) N U U N T N G S ,, , , , , F H G I K J = F H G I K J F H G I K J F H G I K J (2) and N U VV U N P N G V , , F H G I K J = F H G I K J ⇒− F H G I K J = F H I K (3) (b), (c), and (d) are derived in similar fashion.
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