Edexcel IGCSE Physics · Spec 5.8
Specific Heat Capacity: Using the Equation
Worked examples using the specific heat capacity equation.
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Specific Heat Capacity: Using the Equation
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Explained
Specific heat capacity, and what the number is telling you
Specific heat capacity is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius. Its unit, joules per kilogram per degree Celsius, is simply that sentence written in symbols.
Substances differ enormously. Water is about 4200, which is unusually high, while most metals are a few hundred. That means the same energy warms a kilogram of copper far more than a kilogram of water, and it is why water is used in heating systems and as a coolant: it absorbs a great deal of energy for a small rise in temperature.
The equation
Energy transferred equals mass times specific heat capacity times the change in temperature, written Q equals m c delta T.
Keep the units consistent. Mass in kilograms, specific heat capacity in joules per kilogram per degree, temperature change in degrees Celsius, and the answer in joules. A mass given in grams must be converted first.
The temperature change is a difference, so it does not matter whether you work in degrees Celsius or kelvin. A rise of 20 degrees Celsius is a rise of 20 K. This is the one place in thermal physics where converting is not required, because the 273 cancels.
Rearranging it
To find the specific heat capacity, divide the energy by the mass and by the temperature change. To find the temperature rise, divide the energy by the mass and by the specific heat capacity.
As always, substitute before you rearrange. Writing the equation with the numbers in it earns credit on its own, and a rearrangement made before the numbers appear takes the method marks with it if it goes wrong.
Measuring it
Take a block of the material of known mass with a hole for an electric heater and one for a thermometer. Record the starting temperature, run the heater for a measured time, and record the final temperature.
The energy supplied is the power of the heater multiplied by the time, or the voltage times the current times the time. You now have the energy, the mass and the temperature change, so you can find c.
The answer usually comes out too high. Some of the energy escapes to the surroundings rather than going into the block, so the measured temperature rise is smaller than it should be for the energy supplied. Insulating the block and using a lid reduces that, although it never removes it.
What examiners say about this topic
A principal examiner report for Edexcel International GCSE Physics says that many candidates produced an excellent method for determining the specific heat capacity of a liquid. It then explains where those answers stopped short. Most of the marks available were for quoting the bare minimum needed to complete the task, namely listing the measurements and apparatus required for finding the temperature change, the mass and the energy supplied. Full marks could only be awarded if at least one pertinent experimental detail was included.
That is a useful description of how method questions are marked in general. Listing the apparatus and the measurements gets you most of the way. The last mark is for something specific to this experiment, such as insulating the container, stirring the liquid so the temperature is even, or waiting after switching the heater off because the temperature keeps rising for a short while.
When you have written the method, reread it and ask whether any of it could have been written by someone who had never done this particular experiment. If it could, add the detail that only applies here.
Spec 5.8
What you need to know
- Use energy equals m c times the temperature change
- Rearrange it to find c or the temperature rise
- Keep the units consistent
Active recall
Quick check
Answer each question before opening the answer.
What is the equation for thermal energy using specific heat capacity?
Q = m × c × ΔT (energy = mass × specific heat capacity × temperature change).
What does specific heat capacity mean?
The energy needed to raise the temperature of 1 kg of a substance by 1 °C.
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