# Specific heat capacity of metal

1. Aug 26, 2015

### Vir

1. The problem statement, all variables and given/known data
I have 1.5 kgs of silicon with temperature 40 degrees celsius. It is dropped into 3 kgs of water holding temperature 25 degrees celsius. The system is heat isolated from the environment and the final temperature of the system is 26.2 degrees celsius. I need to find the specific heat capacity of silicon.

2. Relevant equations

C = \frac{\mathrm{d}Q}{\mathrm{d}T}

3. The attempt at a solution
Energy lost by metal = energy gained by water:

\Delta U_{m} = \Delta U_{w}
\\
\Delta T_{m} m_{m} C_{m} = \Delta T_{w} m_{w} C_{w}
\\
C_m = \frac{\Delta T_{w} m_{w} C_{w}}{\Delta T_{m} m_{m} }

Now I have one unkown, the specific heat capacity of water. Assuming water to be an ideal gas(which i guess kinda works at lower pressures) I have:

C_w = nR

where $n$ are the amount of moles of water. But here I need the molar mass of water, so that's just another unkown. Is there any way to solve this problem with the given data?

2. Aug 26, 2015

### insightful

Isn't water a liquid in your problem? Can't you just look up the heat capacity of liquid water?

3. Aug 26, 2015

### Vir

I thought gases and liquids had the same properties? The question specifically asks me to figure it out using these data.

4. Aug 26, 2015

### Staff: Mentor

They expect you to know or to look up the heat capacity of liquid water. Look it up and compare it with that of water vapor. Is it really the same?

Chet