Heating Water with vapor at certain pressure

[DelfinDelfin]

Homework Statement

We wish to heat water from 10 °C to 50 °C using vapor at 180 °C and 1.5 bar of pressure. How much cold water do we need to mix with every Kg of vapor to obtain the result?

Homework Equations

I am not sure. I think the problem is related with exergy and energy balance

The Attempt at a Solution

This is the first time I see a problem that relates liquid with gases this way. I only thought about Q = mc (Tf-Ti). So if we knew the energy stored in 1 kg of vapor at 180 C and 1.5 bar, we could assume that the energy is going to be transferred in form of heat to the water, we will have m = Q/(4.186*40 °C). But I don't see how to obtain Q. Or maybe I need a different approach. I will appreciate any suggestions. Thanks

 

[BvU]

Hello DD,

What you want is an energy balance (exergy is not conserved!) - in this case an enthalpy balance.
Write down the situation before mixing on the left and after mixing on the right of an equals sign and solve for the amount of water.