Question 8.3.3: Evaluation of ΔH Using Heat Capacities and Tabulated Enthalp......

air(g, 430°C) → air(g, 100°C)

With Δ\dot{E}_{k}, Δ\dot{E}_{p}, and \dot{W}_{s} deleted, the energy balance is

\dot{Q}=\Delta \dot{H} = \dot{n}_{air }\hat{H}_{air,out}  –  \dot{n}_{air }\hat{H}_{air,in} = \dot{n}_{air }\Delta \hat{H}

Assume ideal-gas behavior, so that pressure changes (if there are any) do not affect Δ\hat{H}.

1. The hard way. Integrate the heat capacity formula in Table B.2.

2. The easy way. Use tabulated enthalpies from Table B.8.
\hat{H} for air at 100°C can be read directly from Table B.8 and \hat{H} at 430°C can be estimated by linear interpolation from the values at 400°C (11.24 kJ/mol) and 500°C (14.37 kJ/mol).

\hat{H}(100°C) = 2.19  kJ/mol\\ \hat{H}(430°C) = [ 11.24 + 0.30(14.37  –  11.24)]  kJ/mol = 12.17  kJ/mol \\ \left. \Large{\Downarrow} \right.\\ \Delta \hat{H} = (2.19  –  12.17)  kJ/mol= –  9.98  kJ/mol

3. The easiest way. In a spreadsheet cell, insert =Enthalpy(“air”,430,100). The value – 9.98 (in kJ/mol) will be returned. In using the spreadsheet, it is absolutely essential to keep track of units by adding explicit notation where appropriate; otherwise the probability of getting units wrong increases substantially.
Whichever way Δ\hat{H} is determined