Question 4.2: Calculate the heat required to raise the temperature of 1 mo...
Calculate the heat required to raise the temperature of 1 mol of methane from 260 to 600°C in a steady-flow process at a pressure sufficiently low that the ideal-gas state is a suitable approximation for methane.
Equations (4.3) and (4.8) together provide the required result. Parameters for C^{ig}_{P} / R are from Table C.1; T_{0} = 533.15 K and T = 873.15 K.
\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)
Then
Q = \Delta H = R \int_{533.15}^{873.15}{\frac{C^{ig}_{P} }{R} dT}
Q =(8.314)\left[1.702(T − T_{0}) + \frac{9.081 \times 10^{-3} }{2}(T^{2} – T^{2}_{0} )-\frac{2.164 \times 10^{-6} }{3}(T^{3} – T^{3}_{0} )\right] = 19,778 J