For steady flow through a heat exchanger at approximately atmospheric pressure, what is the final temperature,

Question

(a) When heat in the amount of 800 kJ is added to 10 mol of ethylene initially at 200°C?
(b) When heat in the amount of 2500 kJ is added to 15 mol of 1-butene initially at 260°C?
(c) When heat in the amount of 106(Btu) is added to 40(lb mol) of ethylene initially at 500(°F)?

Answer 1

If we have set up a spreadsheet to evaluate the heat capacity integral like the example spreadsheet from the lecture notes, we can use it to evaluate the heat capacity integral in each case, and simply vary the final temperature until we get the desired Q.



(a) If 800 kJ is added to 10 mol of ethylene, then So,

so the integral of Cp/R from 200°C (473 K) to the final temperature should be 9622 K. Using our spreadsheet to evaluate this, we get



So, the final temperature is 1374 K.



(b) Similarly, if we add 2500 kJ to 15 mol of 1-butene, we have



Putting the heat capacity coefficients for 1-butene into the spreadsheet and trying final temperatures until we get this value, we get



So, the final temperature is 1414 K.

(c) This is the same, but in English units, in which we can use



The initial temperature of 500 is 533 K. So, we get

And the final temperature is 1203 K = 1705