## Phase change with q=mCsΔT!

Regina Chi 2K
Posts: 51
Joined: Fri Sep 26, 2014 2:02 pm

### Phase change with q=mCsΔT!

Hi, this is actually regarding a specific problem in the textbook (7.39). We are trying to find the final temperature when you put an ice cube at 0°C into water at 45°C. The mass for the ice cube is 50.0 grams and for the water it is 400.0 grams. I understand we use the equation q=mCsΔT, but the part that I need help on is understanding why for the ice cube we use the specific heat capacity of water as a liquid and not as a solid?

martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm

### Re: Phase change with q=mCsΔT!

Specific heat capacity is used for water as a liquid and not a solid because the ice cube (water in solid form) is melting so therefore we would need to compute the heat from fusion and heat once it is a liquid. First, we compute heat as the ice cube melts by using q=n$\Delta$Hfus and once it is melted we find out the heat of it as a liquid using q=mc$\Delta$T. This is why the specific heat capacity is of water as a liquid because at this point we are working with the ice cube that has been melted into water. We add these two heat values (ice cube melting + ice cube melted) in order to find the total heat for the ice cube. The heat for the water already in the container is calculated using -mc$\Delta$T since we are considering it as the surrounding in this experiment.

The set up for this problem should be in the format of qsystem=-qsurroundings. I chose the ice cube to be the system and then found the heat for each. Your final equation should look like this:
(Ice cube) n$\Delta$H + mc$\Delta$T =(water) -mc$\Delta$T

Regina Chi 2K
Posts: 51
Joined: Fri Sep 26, 2014 2:02 pm

### Re: Phase change with q=mCsΔT!

Oh okay. So you're saying when we calculated q=mCsΔT, at that point, the ice cube is already melted into liquid water. And so we would use the specific heat capacity of water to calculate the temperature difference between the two components? This is what you mean right? :)

martha-1I
Posts: 76
Joined: Fri Sep 26, 2014 2:02 pm

Yes. You got it!