Show your work with diagrams (where appropriate) in answering the following ques

Question

Show your work with diagrams (where appropriate) in answering the following questions. Starting from the definition of entropy dS = delta Q_rev/T, show that entropy change for an ideal gas during a reversible process can be given by dS = C_v (dT/T) + nR(dV V). Obtain a corresponding relation for dS in terms of dP and dT by substituting for dV/V in above equation. Integrate between states 1 and 2 to show that for a monatomic ideal gas delta S = S_2 - S_1 is given by: delta S = nR ln [(T_2/T_1)^5/2(P_1/P_2)] Clauses statement of the 2_nd law claims that a cyclic process cannot transfer heat from a low temperature reservoir to a high temperature reservoir. Show that above process violates the equivalent statement of second law for a system and its surrounding: delta S le 0.

Explanation / Answer

F=<ex,exy,exyz>

i...........j.............k

/x...../y......./z

ex........exy.........exyz

curlF=(/y exyz -/z exy)i +(/z ex -/x exyz)j +(/x exy -/y ex)k

curlF=(xzexyz -0)i +(0 -yzexyz)j +(yexy -0)k

curlF=xzexyz i -yzexyzj +yexy k

divF=/x ex +/y exy +/z exyz

divF=ex +xexy +xyexyz

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