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Asked Dec 12, 2019
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11.3. Show that cy and cp are
always positive as long as T is positive.
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11.3. Show that cy and cp are always positive as long as T is positive.

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Expert Answer

Step 1

Heat capacities are defined in terms of quantity of heat and are related to entropy changes.

The relations connecting heat capacities to the quantity of heat Q and the entropy changes (dS) are given as follows:

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dS = dQ/T dS, = dQ, /T = C„dT /T (ôS / ôT), = C, /T.. dS, = dQ, /T = C,dT /T (ôS / ôT), = C, /T... P. ..(1) .(2)

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Step 2

Equation (1) shows that CP is related to the isobaric change in entropy

Equation (2) shows that CV is related to the isochoric change in entropy

From equations (1) & (2), we can write:

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dS, = CpdT /T.. dS, = C,dT /T.. ..(3) .(4)

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Step 3

From the Second Law and Third ...

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Step 3: From the Second Law and Third Laws of thermodynamics, dSee 20. . ..(5) Total S°o=0.. . (6) In general, [Tds = [C,dT = Q. (7) The area under the curve gives | C,dT = Q The curve starts at the origin where T=0 andS=0

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