Thermal properties of materials (5.1.3)
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The specific heat capacity of a substance is defined as:
Specific heat capacity is a measure of how much a material resists changes in temperature.
Specific heat capacity is expressed in units of (joules per kilogram per Kelvin) or (joules per kilogram per degree Celsius) and is denoted by the symbol
The relationship between energy, mass, specific heat capacity, and temperature change is given by:
Where:
- is the thermal energy transferred (in J),
- is the mass of the substance (in kg),
- is the specific heat capacity (in or , and
- is the temperature change (in K or \)
The change in a substance’s temperature depends on:
- Mass: A larger mass requires more energy to achieve the same temperature change because there is more material to be heated.
- Thermal energy: A greater temperature change requires a larger amount of thermal energy.
- Specific heat capacity: Substances with higher specific heat capacities require more energy to raise their temperature.
Substances with low specific heat capacity:
- Heat up and cool down quickly.
- Examples: Metals such as copper and lead have low specific heat capacities, making them efficient conductors of heat.
- These materials are ideal for applications such as cooking utensils, where rapid heat transfer is crucial.
Substances with high specific heat capacity:
- Heat up and cool down slowly.
- Examples: Water has a very high specific heat capacity, making it excellent for storing and transporting heat.
- High value substances are useful in systems such as radiators or thermal insulators, where slow temperature changes are desirable.
Metals such as copper and lead are excellent heat conductors due to the presence of free electrons, which efficiently carry thermal energy. This ability to transfer heat quickly explains their low specific heat capacities.
When calculating specific heat capacity or related energy transfers, it is crucial to use the temperature change not just the final temperature.
Some practical applications of specific heat capacity:
The method of mixture is a practical method to determine a substance’s specific heat capacity using the principle of conservation of energy.
When two substances at different temperatures are mixed in an insulated container, thermal energy is exchanged until they reach thermal equilibrium, that is the same temperature.
The specific heat capacity of one substance can be calculated, provided the mass, temperature change, and the specific heat capacity of the other are known.
Assuming no heat is lost to the surroundings:
This is written mathematically as:
where:
- and are the energy changes of each substance
- and are the masses of the two substances (in kg)
- and are the specific heat capacities (in
- and are the temperature changes (in K or
Rearranging:
Method of mixture experimental method:
- Heat a known mass of the substance whose specific heat capacity you want to estimate. Measure its initial temperature
- Use a substance with a known specific heat capacity, such as water. Measure its mass and initial temperature
- Place the hot substance into the cold substance in a thermally insulated container. Stir gently to ensure uniform mixing.
- Wait until thermal equilibrium is reached, then record the final temperature of the mixture
- Use the equation below to solve for the unknown specific heat capacity of the hot substance.
Question walkthrough
Specific Heat Capacity with Energy Losses
Calculate the specific heat capacity of a metal block heated by an electric heater, accounting for a percentage of the supplied energy lost to the surroundings.
Question walkthrough
Method of Mixtures: Copper and Water
Use conservation of energy to find the specific heat capacity of copper from the equilibrium temperature reached when a hot copper block is placed into water.
An electrical method of determining the specific heat capacity of a substance involves supplying a known amount of energy to a known mass of the substance and measuring the resulting temperature change.
When setting up the experiment, ensure that the apparatus is assembled correctly to minimise systematic errors:
- For solids, the block must have good thermal contact with the heater.
- For liquids, the heater should be fully immersed in the liquid without touching the container.
Place a thermometer in contact with the solid or immersed in the liquid to measure the temperature.
Connect a voltmeter in parallel and an ammeter in series to the heater to measure the energy supplied.
To calculate the total energy supplied to a system when measuring the specific heat capacity of a substance experimentally, use the formula:
where:
- is the current (A)
- is the voltage (V)
- is the time (s) that the power is supplied.
If a joule meter is available, it provides a direct measure of energy supplied, simplifying calculations. Otherwise, take periodic readings of the current and voltage, and calculate average values to use in the formula above.
After switching off the power supply when measuring the specific heat capacity of a substance experimentally, continue to observe the thermometer. The temperature may continue to rise for a few minutes as the heat distributes uniformly throughout the substance. Record the highest temperature reached for accurate results.
The temperature change is equal to:
Be careful to use the temperature change, not the final temperature, in your calculations.
The specific heat capacity can be calculated after measuring the energy supplied the mass of the substance and the temperature change Use the formula:
Ensure all values are in the correct SI units:
- in joules (J)
- in kilograms (kg)
- in kelvin (K) or degrees Celsius
Points to remember when measuring specific heat capacity experimentally:
- Not all the heat supplied by the heater will be used to raise the temperature of the substance. Some heat is lost to the surroundings. To minimise and account for this:
- Use insulating materials (e.g. foam or cloth) around the block or beaker to reduce heat loss.
- Note that any heat loss leads to an overestimate of as is effectively larger than the heat absorbed.
- The voltage and current supplied may fluctuate during the experiment, leading to inaccuracies in the energy calculation. To improve reliability:
- Take periodic readings of and throughout the heating process.
- Calculate the average values for and before substituting them into the formula for the energy transferred.
- For solids, ensure the heater is inserted properly into the block.
- For liquids, fully immerse the heater in the liquid for uniform heating. Use a stirrer to ensure the temperature rise is even throughout the liquid.
Question walkthrough
Designing an Experiment to Measure Specific Heat Capacity
Design a full experimental method using an immersion heater and joule meter to find the specific heat capacity of water, including sources of error and improvements.
Energy is required to change the state of a substance.
When a change of state occurs, energy is supplied to overcome intermolecular forces, not to increase temperature – the temperature remains constant.
The diagram below illustrates the key state changes to remember:
It is useful to note that there is an additional state of change called deposition, where a gas changes directly into a solid without passing through a liquid phase. However, knowledge of this change of state is not required for your exams.
An example of deposition is water vapour in the air depositing as a solid, crystalline frost on a window in cold conditions, bypassing the liquid water state.
The energy required to change the state of a substance without altering its temperature is called latent heat. It is a property that varies depending on the material and state change.
The latent heat of fusion is the amount of energy required to change 1 kg of a substance from a solid to a liquid without a change in temperature.
Energy is required to overcome some of the intermolecular forces holding the solid together, allowing the particles to move more freely in the liquid state.
- Melting: Energy is absorbed to break some intermolecular bonds, allowing the solid to turn into a liquid.
- Freezing: The same amount of energy is released when a liquid solidifies, as bonds reform.
- For water: The latent heat of fusion is , meaning 330 kJ is needed to melt 1 kg of ice at
The latent heat of vaporisation is the energy required to change of a substance from a liquid to a gas without a change in temperature.
Energy is required to completely break the intermolecular forces, allowing particles to move freely as a gas.
- Boiling/evaporation: Energy is absorbed to completely separate molecules.
- Condensation: The same amount of energy is released when a gas turns back into a liquid.
- For water: The latent heat of vaporisation is , meaning is needed to turn 1 kg of water into steam at This means evaporating of water requires about 7 times more energy than melting the same amount of ice.
The energy required for a substance to change state can be calculated using the formula:
Where:
- is the thermal energy supplied or released (J),
- m is the mass of the substance (kg), and
- L is the specific latent heat .
Substances with low latent heat values change state more easily, requiring less energy. Substances with low latent heat can be used for precise temperature control.
Substances with high latent heat values are more stable during state changes, making them useful in thermal storage or cooling applications. Water’s high is why sweating effectively cools the body.
Heating curves show how the temperature of a substance changes as heat is supplied.
Heating curves demonstrate how temperature remains constant during state changes.
When a substance is melting or boiling, all of the energy supplied is being used to change its state, not to raise its temperature, so the temperature remains constant.
While the temperature is constant, the latent heat equation applies:
allowing the latent heat to be determined.
Question walkthrough
Specific Latent Heats of Fusion and Vaporisation
Calculate specific latent heats of fusion and vaporisation from electrical heating data, and explain why vaporisation requires much more energy than fusion.
The specific latent heat of a substance can be determined by measuring:
- The energy supplied to the substance
- The mass of the substance that changes state.
Then rearranging the formula below to make the subject:
Method for measuring the specific latent heat of fusion of ice:
- Place ice cubes in a funnel with filter paper, above a beaker, to isolate the melted water from the ice block.
- Use two beakers:
- Beaker A collects water from ice melted by the immersion heater and by the surrounding air.
- Beaker B collects water from naturally melting ice exclusively.
- Heat the ice with an immersion heater and ensure the electrical circuit is set up for accurate ammeter and voltmeter readings.
- Record the current voltage and heating time
- After a set time, measure the mass of water in both beakers with an electronic balance.
- Isolate the mass melted by the heater alone by calculating the difference in mass readings.
- Calculate the specific latent heat fusion of ice:
Sources of error:
- Filter paper absorbs water: Use non-absorbent material if possible.
- Incomplete thermal equilibrium: If ice is not at some energy is used to raise its temperature before melting begins.
Method for measuring the specific latent heat of vaporisation of water:
- Use a double-walled glass vessel to reduce heat loss and focus energy on vaporisation.
- A condenser ensures the vapour is collected efficiently for mass measurements.
- Collect condensed vapour: Ensure that the entire vapour from the liquid is condensed and collected to accurately measure its mass.
Sources of error:
- Heat loss in the condenser: If vapour escapes before condensing, the mass of collected water will be underestimated, resulting in a higher latent heat value
- Energy loss to surroundings: Not all energy from the heater goes into vaporisation; some heats the environment, causing overestimation of
Potential sources of error common to both the method for measuring the specific latent heat of fusion of ice and the method for measuring the specific latent heat of vaporisation of water are listed below.
- Heat loss to the surroundings is a major source of error in both and measurements. To minimise it:
- Use insulating materials for beakers and vessels
- Limit the system’s exposure to open air
- Conduct the experiment in a draught-free environment.
- Ensure the mass balance is zeroed correctly before weighing substances or collecting water.
- Measure voltage and current periodically and calculate an average to account for fluctuations in the power supply.
- Always monitor the temperature closely to ensure no unintended heating occurs beyond the state change point.
- Latent heat of fusion: Ice remains at while it melts. Ensure the thermometer shows no temperature rise during the process.
- Latent heat of vaporisation: water remains at (at standard pressure) while it boils.
After calculating or compare the value with known values for the substance (e.g. water has values of and to assess the accuracy of your experiment. Large deviations could indicate heat loss or instrument errors.