Latent heat of vaporization problem?

Question

What mass of steam that is initially at 120°C is needed to warm 370 g of water and its 300 g aluminum container from 20°C to 50°C?

Answer 1

Considering water and aluminum as one system,
the energy balance gives delta U = 0;

Therefore

Mwater *Cvwater* (T2 - T1,w) + Maluminim* Cvaluminum* (T2 - T1,a) = 0, where T2 = 50oC, T1,w = 120oC, T1,a = 20oC, Mi = Mass of component i, and Cvi = heat capacity of component i at constant volume.

With the given information, and looking for the heat capacities in a table, you can solve for Mwater.

Answer 2

First, you're going to need to know or find several values. YOu'll need the specific heat of aluminum so that you can calculate how many joules of heat are needed to raise the temperature of the water and the aluminum container. Once you've figured that out (using mass X c X change in temperature), you'll also need the specific heat of steam and the heat of vaporization of water. WIth both of those, you can ultimately calculate how much steam you'll need to provide the energy required to raise the temp of the other stuff....Hope this helps a little...