- #36
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Not really. Between T1 and T2, we have $$m\frac{dh}{dt}=mC^*\frac{dT}{dt}=RHS$$where C* is as I wrote it in post #34. h is the enthalpy per unit mass.casualguitar said:Ahh I see my apologies, yes what I did above is right except I forgot to replace ##T## with the derivative ##\frac{dT}{dt}## on the right. Should it not be (adding in m below the line. I guess you're leaving it out for me to fill it in):
$$C^*=\frac{[C_{PL}(T_{sat}-T_1)+\Delta h_{vap}+C_{PV}(T_2-T_{sat})]}{m(T_2-T_1)}$$
For between T1 and T2, I get $$m=\frac{V}{\left[v_l+\left(\frac{RT_2}{PM}-v_l\right)\left(\frac{T-T_1}{T_2-T_1}\right)\right]}$$casualguitar said:So m is constant outside the phase change zone. Inside the 'phase change' zone as you said its:
$$m=\frac{V}{v_lX+\frac{RT_{sat}}{PM}(1-X)}$$
I think we want the bottom line (average specific volume) to linearly increase from ##v_l## to ##v_g## over the interval ##T1 \leq T \leq{T2}##, so we could just replace ##1-X## with ##\frac{T-T1}{T2-T1}##, to give:
$$m=\frac{V}{v_l(1-\frac{T-T1}{T2-T1})+\frac{RT}{PM}(\frac{T-T1}{T2-T1})}$$