**The Goal: **Calorimetry is the study of how the heat lost by one body is gained by another. Early studies of heat defined it as a 'caloric fluid'; and heat does seem to flow. We have borrowed the term calorie to define a quantity of heat energy: 1cal = 4.2J. (1000 calories is 1 Calorie, the kind we eat). You will use calorimetry to predict the temperature of a mixture.

**The Method: **Hot water will be mixed with cold water. You will predict mathematically the final temperature, then check it experimentally.

**The Theory: **It is a basic law of thermodynamics that heat flows from high temperatures to low tempertures. Therefore, if a substance at a high temperature is mixed with something cooler, the hotter object cools and the cooler object heats up. To understand how an object has heat we must define a quantity called the Specific Heat Capacity: c. It is a quantity that a substance possess, like weight, color, or hardness. Substances like water have very high specific heats while air has a very low c. One uses a hot water bottle, not a hot air bottle, to warm one's feet on a cold night.

There is a math equation which uses c and mass to find the energy necessary to raise or lower the temperature of something. It goes like this:

Q = mc (T_{f} - T_{i})

Q is heat (don't ask me why). The mass is m, T_{i} is the starting temperature, and T_{f} is the temperature of the object after heat is added or removed. For instance, if the starting temperature is 20^{o}C for 1kg of water, which has a specific heat of 1cal/gram C^{o}, if you add 10 calories of heat the final temperature will be 30^{o}C.

Using the idea that heat flows from how to cold and this equation:

mc (T_{h} - T_{f}) = mc (T_{f} - T_{c})

heat lost = heat gained

one can predict the final temperature of a mixture. The T_{f} is the same for both, but T_{i} is different for each substance in your experiment, the hot and cold temperatures, respectively. **Predict means to do the math before the experiment, not consult the Psychic Friends Hotline!**

One source of error with this kind of experiment is that some heat leaks out of the mixture container before it can warm up the cooler substance.

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