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Unformatted text preview: i a segment o path 2. Hence, the integrand f ( p, T ) = pT is always greater along path 1. Thus, the two integrals over V , which have the same upper and lower limits, are not equal to each other: Z 1 pT dV > Z i a pT dV = Z 2 pT dV . We see then that R TdQ is greater along path 1 than path 2 and is thereore path-dependent. Similarly, one can show that or R dQ/T 2 = R pdV/T 2 + R nC V dT/T 2 , the second term on the right is path-independent, while or the rst term Z pdV/T 2 = nR Z dV TV , we have nR Z 2 dV TV = nR Z i a dV TV > nR Z 1 dV TV , since the average value o 1 /T is greater along along the i a segment o path 2 than on path 1. Consequently, R dQ/T 2 is less along path 1 than path 2 and is thereore path-dependent....
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- Fall '08