Experimental measurements of heat capacities are often represented in reference

Question

Experimental measurements of heat capacities are often represented in reference works as empirical formulas. For graphite, a formula for the heat capacity of constant pressure that works well over a fairly wide range of temperature is, for one mole, C_{p}=a+bT-rac{c}{T^{2}}, where a = 16.86 J/K, b = 4.77*10-3J/K2, and c= 8.54*105 J*K. Suppose a mole of graphite is heated in an isobaric process from 298K to 500K. (a) Calculate the increase in entropy during this process. The entropy of graphite at 298K is S=276 J/K (b) How much energy was needed to heat up the graphite?

Explanation / Answer

Cp = a + bT - c/T2

change in entropy = CpdT/T (integration over T= 298 to T = 500)

=integration (a/T + b - c/T3)dT

= (a ln500/298 + b(500-298) + c/2(500)2- c/2(298)2)

put the values to get the answer.

B) ENERGY NEEDED = integration CpdT = a(500-298) + b(5002 - 2982) + c(1/500 - 1/298)

put values and get answer

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