Questions regarding HW6

Some questions and answers-

The table C.1 has values of B divided by 10^3, but the examples in the book have 10^-3. Could that be a typo?

What the book is reporting is the value of B times 10^3, so that the actual value of B is a factor of 10^3 smaller. Think of the number listed in the table as a value x. Then, we have B*10^3 = x so that B = x * 10^-3. Similar for C and D.

I am trying to work on problem 4.2 part a, using the example 4.3 as a guide. So for the iteration of the mean heat capacity over R, how can I compute it without having a value for tau? Should I assume first it equals to 1, starting with T = Tzero, then getting a value for heat capacity, plug it into T = deltaH/Cp + Tzero. Then using the new T, with new tau , get another value for Cp, then another value for T and so on?

Yes, exactly. Remember, the mean heat capacity depends on both the initial and final temperatures. Consider constant pressure heating where the heat duty is specified. In this case, the first law is:

Delta H = Q/n

We can rewrite Delta H using the mean heat capacity and the temperature change:

(Tf - T0) Cpavg = Q/n

We can solve this for Tf, but it is highly nonlinear in Tf. Why? This is because Tf not only appears in the temperature difference, but it is part of the expression for (by way of tau). Setting up an iteration helps us solve this nonlinear equation:

Tf = (Q/n) /Cpavg + T0

You start with a guess for Tf and plug it in. The easiest guess is just to use T0. Then, you use this equation to continue to get new guesses for Tf until you converge on one value. At that point, you have found the value of Tf that solves the original equation.

Cheers,
MSS