# Heat capacity of water -- experimental determination

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1. Mar 2, 2015

### sunquick

1. The problem statement, all variables and given/known data
A quantity of water in a beaker of negligible thermal capacity is cooled to a few degrees below freezing point. The beaker is then placed in a warm room, and the times recorded at which it is at various temperatures as it gradually warms. The observations were:

temperature/ºC time/min:
-3.0 0
-2.0 0.93
-1.0 1.89
0 2.92
.....
0 169.72
1.0 171.84
2.0 174.04
3.0 176.34

2. Relevant equations
$$Q=C \Delta T$$
$$Q= L$$
$$Q= P \Delta t$$

3. The attempt at a solution

My question concerns part b)
I assume the power delivered to the system is constant.
So $$Q=C \Delta T = P \Delta t$$ or
$$\frac{\Delta t}{\Delta T} = C/P = const$$

So I fit a straight line to the experimental points to determine the slope and so to know C/P.
There will be two heat capacities, one for ice and the other for liquid water. I can determine the ratio o C_ice / C_water, and also of the latent heat necessary to melt the ice by noting that

$$P \frac{\Delta t_1}{\Delta T} = C$$
$$P \Delta t_2 = L$$
$$\Delta t_2 \frac{\Delta T}{\Delta t_1} = L / C$$

I can find the heat capacities and latent heats with respect to one another, but I can't seem to know how find one of them in "absolute terms". My question is if that is possible, and what other quantitative results can be obtained from the observations?

2. Mar 2, 2015

3. Mar 2, 2015

### sunquick

Sorry I forgot tho type that part of the problem:

a) Explain the general form of the experimental results.
b) What quantitative results can you deduce from the observations?

For part a) I have to explain that heat is transfered to the ice, increasing its temperature, till it reaches 0ºC. Then it stays at that temperature untill all the ice has melted away, because all the heat entering the system is going into changing the phase of the water instead of increasing its temperature. Once the ice has melted, the temperature rises again, this time at a different rate than before because water has a different specific heat capacity than ice.

4. Mar 2, 2015

### haruspex

Then I think you are finished. As you say, you cannot determine the heat capacities of the water sample in its different phases, let alone the capacities per unit mass. All you can provide is the ratios between them.