Given these data, compute the heat of fusion of water. The...

Given these data, compute the heat of fusion of water. The specific heat capacity of water is $4.186 \mathrm{J} / \mathrm{cg} \cdot \mathrm{K}$ ). $$ \begin{array}{cl} \hline \text { Mass of calorimeter }= & \text { Specific heat of calorimeter }= \\ 3.00 \times 10^{2} \mathrm{g} & 0.380 \mathrm{J} /(\mathrm{g} \cdot \mathrm{K}) \\ \text { Mass of water }= & \text { Initial temperature of water and } \\ 2.00 \times 10^{2} \mathrm{g} & \text { calorimeter }=20.0^{\circ} \mathrm{C} \\ \text { Mass of ice }=30.0 \mathrm{g} & \text { Initial temperature of ice }=0^{\circ} \mathrm{C} \\ & \text { Final temperature of calorimeter }= \\ & 8.5^{\circ} \mathrm{C} \\ \hline \end{array} $$

Given these data, compute the heat of fusion of water. The specific heat capacity of water is $4.186 \mathrm{J} / \mathrm{cg} \cdot \mathrm{K}$ ).
$$
\begin{array}{cl}
\hline \text { Mass of calorimeter }= & \text { Specific heat of calorimeter }= \\
3.00 \times 10^{2} \mathrm{g} & 0.380 \mathrm{J} /(\mathrm{g} \cdot \mathrm{K}) \\
\text { Mass of water }= & \text { Initial temperature of water and } \\
2.00 \times 10^{2} \mathrm{g} & \text { calorimeter }=20.0^{\circ} \mathrm{C} \\
\text { Mass of ice }=30.0 \mathrm{g} & \text { Initial temperature of ice }=0^{\circ} \mathrm{C} \\
& \text { Final temperature of calorimeter }= \\
& 8.5^{\circ} \mathrm{C} \\
\hline
\end{array}
$$

Key Concepts

Energy Conservation in Thermal Processes

This principle states that energy in an isolated system remains constant, meaning that the total heat lost by one component is equal to the heat gained by another. This concept is critical in solving problems involving heat transfer and phase changes in calorimetry.

Calorimetry

Calorimetry is the technique used to measure the amount of heat exchanged in physical or chemical processes. It involves tracking the heat flow between substances, often by monitoring changes in temperature of a calorimeter and its contents.

Heat of Fusion

This is the amount of energy required to change a substance from a solid to a liquid at its melting point without changing its temperature, typically expressed per unit mass. It is essential for processes involving phase changes, such as melting ice into water.

Specific Heat Capacity

This is a property of a material that defines the amount of heat required to raise the temperature of a unit mass of that material by one degree Celsius (or Kelvin). It plays a crucial role in determining how much energy is needed to effect temperature changes in substances.

Transcript

00:01 In this example, they ask us to find the heat of fusion of water.

00:07 And they tell us that we have a calorometer, water, and ice, and this enclosed system.

00:15 So we're just going to assume that we're not losing any heat or energy to the environment or if we are that it's negligible.

00:23 So first thing we have to do is we're going to have to find the heat lost by the calorometer.

00:30 We know that will be equal to the mass of the calorometer times the heat capacity of the calorometer times the change in temperature.

00:42 We're told that both the calorometer and the water start at an initial temperature of 20 degrees celsius and have a final temperature of 8 .5 degrees celsius.

01:00 So change in temperature is just going to be our final.

01:04 Will minus our initial.

01:06 That will give us negative.

01:08 0 .5 degrees celsius, which is also equal to a change of 11 .5 degrees, or 11 .5 kelvin.

01:23 So plugging all the values we have, we have the mass of our calerometer, as well as the heat capacity of our calerometer.

01:31 Plug that into our equation, and we get a loss of heat of 1 ,311 jules.

01:49 Next, we want to find how much heat we lose from our water.

01:56 So that's going to be the mass of the water times the heat capacity of the water, times the change in temperature, which we already said is the same as the change in temperature for our calorometer...

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