Question 4.3: What is the final temperature when heat in the amount of 400...

If ΔH is the enthalpy change for 1 mol, Q = n ΔH, and

\Delta H = \frac{\varrho }{n} = \frac{400\times 10^{6} }{11,000} =  36,360  J· mol^{−1}

Then for any value of T, with parameters from Table C.1 and R = 8.314 J· mol^{−1}·K^{−1}:

\frac{\left\langle C_{P} \right\rangle_{H} }{R}= MCPH (530, T; 3.578, 3.020 \times   10^{-3} , 0.0, −0.186 \times  10^{5} )

This equation and Eq. (4.11) together can be solved for T, yielding T = 1234 K.

T = \frac{\Delta H}{\left\langle C_{P} \right\rangle _{H} } +T_{0} (4.11)

A trial procedure is an alternative approach to solution of this problem. One sets up an equation for Q by combining Eqs. (4.3) and (4.8),

\varrho = \Delta H = \int_{T_{1} }^{T_{2}}{C_{P} dt }      (4.3)

\int_{T_{0}}^{T }{\frac{C_{P} }{R} dT} =A (T-T_{0}) + \frac{B}{2}(T^{2} – T^{2}_{0} ) + \frac{C}{3} (T^{3} – T^{3}_{0})+ D \left(\frac{T-T_{0}}{TT_{0}} \right)         (4.8)

with T as an unknown on the right. With Q known, one merely substitutes a rational succession of values for T until the known value of Q is reproduced. Microsoft Excel’s Goal Seek functionis an example of an automated version of this procedure.