Question 18.4: Estimate the heat transfer rate required to heat low-pressur...

The system here is just the gas in the heating zone. Neglecting the flow stream kinetic and potential energies, the energy rate balance for this system reduces to

\dot{Q} + \dot{m} (h_\text{in} − h_\text{out}) = 0

so that

\dot{Q} = \dot{m} (h_\text{in} − h_\text{out}) = \dot{m}c_p (T_\text{out} − T_\text{in})

For \text{CC1}_4, b = 5; consequently, F = 3b = 15. Then, Eq. (18.28) gives

c_p = R+ c_v = (1 + \frac{F}{2}) R            (18.28)

c_p = (1 + 15/2)R = 8.5 × R

Now, the molecular mass of carbon tetrachloride is

M = 12.0 + 4(35.5) = 154  \text{kg/kgmole}

and its gas constant is

R = \frac{ℜ}{M} = \frac{8.3143  \text{kJ/(kgmole.K})}{154  \text{kg/kgmole}} = 0.0540  \text{kJ/(kg.K)}

so

c_p = 8.5 [0.0540  \text{kJ/(kg.K)}] = 0.459  \text{kJ/(kg.K)}

Therefore,

\dot{Q} = (1.00  \text{kg/min}) [0.459  \text{kJ/(kg.K)}] (1200. − 500. \text{K}) = 321  \text{kJ/min}