# Do you use internal energy or enthalpy to calculate energy required to boil water from saturated liquid to saturated vapor

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

• 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? Nov 1, 2020 at 12:43

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.
$$h=u+pv$$
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.