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problem-solution-6

# problem-solution-6 - Chem 444 Instructor Nancy Makri...

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Chem. 444 Instructor: Nancy Makri PROBLEM McQ 20-6 Calculate q rev and S for a reversible cooling of one mole of an ideal gas at a constant volume V 1 from P 1 , V 1 , T 1 to P 2 , V 1 , T 4 followed by a reversible expansion at con- stant pressure P 2 from P 2 , V 1 , T 4 to P 2 , V 2 , T 1 (the final state for all the processes shown in Figure 20.3). Compare your result for S with those for paths A, B+C, and D+E in Figure 20.3. Beginning with the first law of thermodynamics: dU q w δ δ = + We recall that for an ideal gas U α T and that for the overall process T i = T f so, 0 dU q w δ δ = = - And with a little more work, 1 2 2 1 1 1 2 2 2 1 0 ( ) V V V rev V V V q w PdV PdV P dV P V V = - = + = + = - It then follows for the entropy that rev dq PdV RdV dS T T V = = = where n = 1 mole as suggested by the problem statement. It then follows that 2 1 1 1 2 1 ln V V V V RdV RdV V S R V V V = + = ÷ The process described in this problem and in Figure 20.3 trace out different paths in PV -space but have the same final and initial points. Hence the heat evolved, being de-

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