Specific Heat and Thermal Conductivity
Introduced| English | Meaning |
|---|---|
| specific heat capacity/spəˈsɪfɪk hiːt kəˈpæsɪti/ | The energy needed to raise the temperature of one kilogram of a substance by one kelvin or one degree Celsius. |
The sand scorches your feet, but the sea stays cool
- On a summer beach the sand burns your feet while the water beside it is refreshingly cool.
- Same sunshine — but water needs far more energy to warm up than sand does.
- How much heat a material needs per degree is its specific heat capacity 比热容.
- A related idea, thermal conductivity, sets how fast heat travels through it.
The heat equation
- The heat to change a temperature is $Q = mc\Delta T$.
- $m$ is the mass, $c$ the specific heat capacity, and $\Delta T$ the temperature change.
- A high $c$ (like water) means a lot of energy per degree — it heats and cools slowly.
- A low $c$ (like metal) means little energy per degree — it heats up fast.
Heat different materials
Change the material and mass and see how much heat is needed for a given temperature rise.
How much heat warms $2\ \text{kg}$ of water by $10\ ^\circ\text{C}$? ($c = 4200\ \tfrac{\text{J}}{\text{kg}\cdot^\circ\text{C}}$.) Answer in $\text{J}$.
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$Q = mc\Delta T = 2 \times 4200 \times 10 = 84\,000\ \text{J}$.
The heat needed to warm a mass is $Q = m c \_\_$ (fill in the missing symbol).
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$Q = mc\Delta T$ — mass times specific heat times temperature change.
Why water is special
- Water has an unusually high specific heat, so it stores lots of heat with little temperature change.
- This is why the sea warms and cools slowly, moderating coastal climates.
- It is also why water is used as a coolant in engines and power plants.
- Metals, with low $c$, respond to heat quickly — good for cooking pans.
A material with a high specific heat capacity:
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High $c$ (like water) means a lot of energy per degree, so slow temperature change.
Why is water often used as a coolant in engines?
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Water's high $c$ soaks up heat without getting very hot — ideal for carrying heat away.
Select all true statements.
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The first three are true. The last describes conductivity, not specific heat.
Thermal conductivity
- Thermal conductivity measures how fast heat flows through a material.
- Metals conduct heat quickly (they feel cold because they draw heat from your hand).
- Insulators like wood, foam and air conduct slowly, trapping heat.
- Conductivity is about the speed of heat flow; specific heat is about how much heat to warm up.
Specific heat and thermal conductivity are the same property.
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Specific heat is energy per degree; conductivity is how fast heat flows through — different ideas.
Don't confuse specific heat with thermal conductivity. Specific heat ($c$) is how much energy a material needs to change its temperature; conductivity is how fast heat passes through it. Water has a high specific heat but is a poor conductor.
How much heat warms $2\ \text{kg}$ of water by $10\ ^\circ\text{C}$? (Take $c = 4200\ \tfrac{\text{J}}{\text{kg}\cdot^\circ\text{C}}$.)
- $Q = mc\Delta T = 2 \times 4200 \times 10 = 84\,000\ \text{J}$.
The same heat would warm a metal of much lower $c$ far more than $10\ ^\circ\text{C}$.
Specific heat capacity $c$ is the heat per kilogram per degree: $Q = mc\Delta T$. A high $c$ (water) resists temperature change; a low $c$ (metal) heats up fast. Thermal conductivity is a different property — how fast heat flows through a material.
Write from a heat transfer of 1200 J
- A 0.40 kg sample has specific heat capacity 500 J per kg per degree.
- It warms by 6 degrees. Find the heat gained.
A 0.40 kg sample with specific heat capacity 500 J per kg per degree warms by 6 degrees. How much heat does it gain, in joules?
0.40 times 500 is 200, and 200 times 6 is 1200.
How much heat does the sample gain?
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Mass times specific heat times the temperature change is 1200 J. Other options — 84000 J (the lesson water sample); 500 J (the specific heat capacity used as the heat).