Core Unit IV: Heat

B. Specific Heat Capacity and Latent Heat

Key Concept

Specific heat capacity is the quantity of heat required to raise the temperature of a unit of mass of a substance by a unit change in temperature.

or, Q = mcT

where Q is the change in heat content in Joules, m is the mass in kg, c is the specific heat capacity in J/(kg°C), and T is the change in temperature in °C or K.

The derived unit for c, the specific heat capacity, is J/(kg°C)

The specific heat capacity of a substance depends on its molecular structure and on its phase.

The specific latent heat of a substance is the quantity of heat energy required to change the state of a unit mass of a substance.

E_L= ml where E_L is the heat transferred, in joules, m is the mass, in kilograms, and l is the latent heat in joules per kilogram.

The SI unit for specific latent heat is J/kg.

The specific latent heat of fusion is the quantity of heat energy released when 1 kg of a substance solidifies (i.e. fuses) without changing its temperature.

The specific latent heat of vaporization is the quantity of heat energy needed to vaporize 1 kg of a substance without changing its temperature.

Water has one of the largest specific latent heats of fusion of all substances.

Water exhibits anomalous behaviour. From 0 °C to 4 °C it contracts as heated. It also expands when it freezes. The expansion results in a decrease in density, allowing ice to float on water. Also, water has a high specific heat capacity compared to other liquids.

The unique physical characteristics of water lead to many interesting and important applications. (Several should be discussed. Wherever possible, suggest some of the environmental implications of these characteristics of water.)

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: specific heat capacity, specific latent heat, specific latent heat of fusion, specific latent heat of vaporization.

2. Solve problems involving specific heat capacity and specific latent heat.

3. Distinguish between specific heat capacity and specific latent heat.

4. Use the correct units for specific heat capacity and specific latent heat.

5. Identify several unique physical properties of water.

6. Suggest some environmental implications leading from the physical properties of water.

Teaching Suggestions, Activities and Demonstrations

1. Perform an activity to determine the specific heat capacity of a substance. See the next activity for an example of how this could be done.

2. Place a measured volume of cold water into a calorimeter. Measure its initial temperature. Heat a metal object of known mass in a beaker of boiling water long enough so that the metal object reaches a temperature of the boiling point of water. (When the metal object is first placed into boiling water, the water may stop boiling. Wait until the water has reached the boiling point once again.) Transfer the hot metal object into the calorimeter. Record the final temperature of the water in the calorimeter after heat transfer has taken place. Determine the specific heat capacity of the metal. Repeat using different types of metal. (Before transferring the metal to the calorimeter, attach thread to it. Transferring the metal using cold metal tongs acts as a heat sink.) Based on the experimental results, qualitatively develop the Principle of Heat Exchange, for section C on thermodynamics.

3. Perform an activity to investigate the specific latent heat of fusion (or the specific latent heat of vaporization, or both) for a given substance.

   Repeat the above experiment with ice to find the specific latent heat of ice.

4. Give students some examples of the unique physical characteristics of water and how they have made it possible for life to exist on this planet. For example, brainstorm to establish what kinds of things might happen if water in a large lake froze solid in the winter, or if water froze at lower temperatures.

5. During a short break between classes, suppose a person wants to drink a cup of coffee. Design an experiment to determine if it is better to add milk (or cream) and then wait five minutes before drinking it, or to allow the black coffee to cool for five minutes and then add the milk (or cream). In which situation would the coffee be the coldest after the five minute interval?

   Other variables, such as the type of container the coffee is poured into, or the initial temperature of the coffee, and the type of coffee used (percolated, drip, or instant), etc., should all be fully controlled.

6. Using three different metal samples having the same mass, heat them all in water until each one reaches the boiling point of water. Carefully remove each one and place it on a sheet of paraffin wax. Allow them all to cool. Observe how far each sample has been imbedded into the wax. The metal with the highest specific heat capacity will have been able to melt away the most wax and imbed itself the deepest into the wax. This is a very simple but effective demonstration or student group activity which reinforces this concept.

7. Using brainstorming, suggest some of the ways in which the unique physical characteristics of water lead to a number of interesting and practical applications.

8. Waste heat from industrial processes sometimes causes thermal pollution. Research ways in which waste heat is being put to better use than by releasing it into the environment. Use webbing to link this activity with Science 10 or Biology 20.

9. Design a passive solar water heater. Design it to optimize the amount of heat energy that can be absorbed by a given quantity of water. Compare the efficiency of the designs developed by different groups.