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The water stream is heated in a boiler, at some constant pressure. When entering the boiler, the water flow is in a saturated liquid state. After heating the outflow fluid has become saturated vapor. My question is if I want to calculate how much heating energy is needed, do I use $$Qb = Ug - Uf$$ or $$Qb = hg - hf$$

U is Internal Energy, h is enthalpy, and f and g refer to saturated liquid and saturated gas

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  • $\begingroup$ You are talking about an open. continuous flow system. What does the open system (control volume) version of the 1st law of thermodynamics tell you for such as system? $\endgroup$ Nov 1, 2020 at 12:43

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Use enthalpy. $Q_b$ is then $h_{fg}$ from the steam tables. $h_{fg}$ is the latent heat of vaporization, the heat required per unit mass to convert the mass from saturated liquid to saturated vapor.

Specific enthalpy and specific internal energy are related by

$$h=u+pv$$

Hope this helps.

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If you apply the open system version of the first law of thermodynamics to this system, you obtain $$\dot{Q}=\dot{m}(h_{out}-h_{in})$$where $\dot{Q}$ is the rate of heat transfer to the boiler contents, $\dot{m}$ is the mass rate of flow of water through the boiler, $h_{out}$ is the specific enthalpy of the exiting steam and $h_{in}$ is the specific enthalpy of the entering water.

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