Question

please answer all parts (a,b, and c)

In class we showed that for a Carnot cycle for an ideal gas (Lecture 8, page 10), the following identity follows: Sigmai qi/Ti = q1/T1 + q2/T2 = 0, Where qi, is the (reversible) heat associated with each isothermal step. As we shall see next week, we will be able to identify each of these terms as entropy contributions, DeltaSi = qi/Ti, such that they add up to zero in a cycle, giving us the hint that S is in fact a state function. Consider Fig. 1, which is a generalization of the Carnot cycle for three heat reservoirs. Here, 1 rightarrow 2, 3 rightarrow 4, 5 rightarrow 6 are isotherms at three different temperatures Th, Tm, and Tc, respectively, while 2 rightarrow 3, 4 rightarrow 5, and 6 rightarrow 1 are adiabats. The whole cycle is reversible and going clockwise (it is a heat engine rather than a refrigerator). Make the analogous table to tlie one in Lecture 8, page 9, where you showr q, w, DeltaU for each step of the cycle. Leave the expressions in terms of n, Th, Tm, Tc, V1,---, V6. V6/V5 = V1/V2 V3/V4. See Lecture 8, page 10. Generalize Eq. (1) to this cycle, i.e., sigmai qi/Ti = qh/Th + qm/Tm +qc/Tc = 0.

Answer 1

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