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AS5300_exercise1_2010_soln

AS5300_exercise1_2010_soln - .P~1 S.~Ca CAClA ~c:J(Pr< 5...

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· '. . P~1 S.~C a- \ C A ClA ~~c:J) (Pr<; 5 SCf\)) £?\e # - L ~U,l-1 .. U J ~ . ~~ t L ~\ e tNf d~ - J - t: + J - \f - T ~ -- e i T J. . s l e, 'V ' NI) ~S - \ dE:: 'T - ~ N' I ' Co~CJ Q) ~J (i) t'0 . ... ~s \ ' - ~N I --- ""\ E'llf - Nits I J or ,. L \ ~ - ® ~~o •..• . . . CD l "" WN <r\ a ~ " "-~ ) . I I L t,) L N J .. N~ ® ,. . J S', . ? d ' ~ 1 - !c •... , - t § l 6>E: \ J - ¥ - + - ~&~ \ 0\1' - \\ f d - ¥- I ' ~Nl ~;N l ~ , -¥j M~ ts-
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1 Exercise # 1 Que # 4: a.) We have, ܶ݀ݏ ൌ ܧ݀ܶ ൅ ݌݀ݒ ൅ ∑ሺμ/ܶሻ ݀ܰ (1) For single specie and assuming there is no chemical change we can ignore the summation term in the above equation. Therefore we will have, ܶ݀ݏ ൌ ܧ݀ݐ ൅ ݌݀ݒ (2) ܶ݀ݏ ൌ ܥݒ݀ܶ ൅ ݌݀ݒ (3) Also we have, ݌݀ݒ ൅ ݒ݀݌ ൌ ܴ݀ܶ (4) From these two equations we will be having, ܶ݀ݏ ൌ ܥ݌݀ܶ െ ݒ݀݌ (5) For constant pressure, dp = 0. The above equation will become, ܶ݀ݏ ൌ ܥ݌݀ܶ Integrating the above equation and putting starting values as T ref and S ref for T and S respectively. We will get, ܶ ൌ ܶݎ݂݁ כ exp ሺሺܵ െ ܵݎ݂݁ሻ/ܶݎ݂݁ሻ The plot will look like as following,
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2 In the above figure, there are two line plotted for the two different reference values and the arrow shows the direction of increasing pressure. For constant volume dv=0. The equation (3) will become, ܶ݀ݏ ൌ ܥݒ݀ܶ Integrating this equation will lead to the following solution, ܶ ൌ ܶݎ݂݁ כ exp ሺሺܵ െ ܵݎ݂݁ሻ/ܥݒሻ The plot will look like as following,
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3 The combined plot for constant P and constant V on T-S diagram is given below,
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