Question 4.3: What is the final temperature when heat in the amount of 400...
What is the final temperature when heat in the amount of 400×106J is added to 11 × 10³ mol of ammonia initially at 530 K in a steady-flow process at 1 bar?
Learn more on how we answer questions.
If ΔH is the enthalpy change for 1 mol, Q = n ΔH, and
ΔH=nϱ=11,000400×106= 36,360 J⋅mol−1
Then for any value of T, with parameters from Table C.1 and R=8.314J⋅mol−1⋅K−1:
R⟨CP⟩H= MCPH(530,T;3.578,3.020 × 10−3,0.0,−0.186 × 105)
This equation and Eq. (4.11) together can be solved for T, yielding T = 1234 K.
T=⟨CP⟩HΔH+T0 (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),
ϱ=ΔH=∫T1T2CPdt (4.3)
∫T0TRCPdT=A(T−T0)+2B(T2–T02)+3C(T3–T03)+D(TT0T−T0) (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.