# How is $Q_s = M_s \times H_{fg}$ derived?

1. Dec 13, 2011

### fubarite

I'm not fully sure if this would go in a "homework" section or the chemistry so I have posted in both.

basically the equation in the title is Qs = Ms times Hfg with
Q being the energy of steam, M being the mass of steam and H being the enthalpy as the saturated steam is between the state of liquid and gas.

This equation is involved in a university experiment of mine and I'd like to know where it's derived from as there doesn't seem to be a simple "energy = mass times enthalpy" expression, I know energy is equal to mass times the specific heat times change in temperature so are these two connected? And if the above is derived from that then how exactly?

2. Dec 13, 2011

### cheme101

Sounds like you're dealing with some kind of vaporizer.

There are two things that heat can do when you add it to a liquid system:
-if the liquid is below its saturation temperature (i.e. boiling point), added heat will increase the liquid temperature (Q = mcpdT).
-once the liquid reaches its boiling point, added heat will vaporize some or all of the liquid. (Q=m(Hfg)
In your case, the liquid is already at its boiling point, so all of the heat energy coming in (i.e. Q) drives evaporation. So you can calculate the heat energy by multiplying the mass of generated steam by the energy required to vaporize it.

That's where the equation comes from.