One Calorie of energy is the heat needed to increase the temperature of 1kg of pure water by 1 degree C. Water heating calculations are based on pure water, but spa water contains impurities, such as dissolved minerals and gasses. Their presence in the water alters its density and mass, so it is necessary to compensate by establishing the exact mass of 1 litre of spa water before performing the math required to find the kilowatts required to heat it.

- Skill level:
- Moderately Easy

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### Things you need

- Thermometer
- Scientific weighing scales

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## Instructions

- 1
Determine the existing temperature of the water and subtract it from the desired temperature. The result is the number of degrees difference between the existing and desired temperatures. For example, if the spa water is at 20 degrees C, and you want to heat it to 1.67 degrees C, the difference is -9.44 degrees C.

- 2
Measure, in kilograms, the mass of one litre of spa water. Multiply this value by the difference in temperature. The result is the number of Calories required to heat the water by the desired amount. For example, 1kg of water requires 15 Calories to heat it by -9.44 degrees C, and 1.1kg of water requires 16.5 Calories to heat it by -9.44 degrees C (1.1 x 15 = 16.5).

- 3
Multiply the result from Step 2 by 1.1622, the number of watt hours equivalent to 1 Calorie. The result is the amount of energy, in watt hours, required to heat 1 litre of spa water to the desired temperature. For example, 18.645 watt hours are required to heat a litre of spa water from 20 to 35 degrees C because 16.5 x 1.1622 = 18.645.

- 4
Divide the result from Step 3 by 1,000 to convert from watt hours to kilowatt hours. For example, heating a litre of spa water from 20 to 35 degrees C requires 0.018645 kilowatt hours of energy because 18.645 divided by 1,000 = 0.018645.

#### Tips and warnings

- One litre of pure water at standard temperature and pressure has a mass of 1 kilogram.
- It takes time to heat water. The energy required is applied over time, so the units must represent time as well as energy. For this reason, kilowatt hours are used rather than kilowatts.
- Do not confuse Calorie, with a capital C, with calorie. A Calorie is also a kcal and is equivalent to 1,000 calories.

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#### References

- University of North Carolina at Chapel Hill; How Many? A Dictionary of Units of Measurement; Russ Rowlett; July 2001
- San Jose State University College of Engineering; ENGR 10 -- Intro to Engineering; 2011
- University of North Carolina at Chapel Hill; How Many? A Dictionary of Units of Measurement; Russ Rowlett; October 2002
- University of Wisconsin-Stevens Point: K-12 Energy Education Program: What is Energy?: Section C. Measuring and Quantifying Energy