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OThurSep25

# OThurSep25 - Thermodynamics 1 A general cycle can be...

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1 Thermodynamics

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2 A general cycle can be divided into small Carnot Cycles. The match is exact in the limit of infinitesimally small cycles. Paths cancel in the interior of the collection and only the perimeter survives. Because the sum of the q/T terms is 0 for every little cycle, the sum of the q/T terms for every little cycle around the perimeter is 0.
3 Entropy Entropy is given the symbol S. The heat in this relationship is reversible and S is of course a state function. Entropy is used to determine the favorable direction of a reaction. Although heat is not a state function, the integral of the heat dq rev , divided by the temperature at which it is transferred is independent of the path and only depends on the initial and final states of the system. T dq dS rev =

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4 An Irreversible Engine For an irreversible engine And therefore in general … 0 < + c c h h T q T q 0 < T dq h c h h c h T T T q q q - < +
5 What is Entropy Things like pressure, volume, internal energy and even enthalpy are easy enough to think about. But what is entropy. Entropy is a measure of disorder. In fact the second law of thermodynamics may be expressed as everything tends towards disorder. Because we said that for a real process it follows that for an irreversible process 0 < T dq T dq S

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6 Entropy and Internal Energy dw dq dU + = dT C dU V = T dq dS = Relate entropy to U, q and w V dV R T dT C dS V + = + = 1 2 1 2 ln ln V V R T T C S V + = Integrate Divide by T and substitute
7 Example Calculate the change in entropy when one mole of an ideal gas expands from 3 liters at 27 °C to 6 liters at 327 °C. C V for this gas is 2.5 R. 1 2 1 2 ln ln V V R T T C S V + = 1 - 1 - mol K J 20 3 6 ln 314 . 8 300 600 ln 314 . 8 5 . 2 = × + × × = S

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8 Entropy changes If entropy is a measure of order then heating a system will increase the amount of disorder, simply because the molecules are charging around faster. Entropy will increase if the number of degrees of freedom increases, i.e.
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OThurSep25 - Thermodynamics 1 A general cycle can be...

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