Thermal equilibrium
Introduced| English | Meaning |
|---|---|
| heat/hiːt/ | Energy transferred between systems because of a temperature difference. |
| thermal energy/ˈθɜːml ˈenədʒi/ | Energy associated with the random motion and interactions of particles in a substance. |
| thermal equilibrium/ˈθɜːml ˌiːkwɪˈlɪbrɪəm/ | A condition in which bodies have the same temperature and no net heat flows between them. |
| net flow/net fləʊ/ | net flow |
A spoon in hot soup
- Put a cold spoon in hot soup: the spoon warms, the soup cools — until they match.
- Energy moved from the hot thing to the cold thing.
- That one-way flow is the key idea of temperature.
Thermal equilibrium route
Watch energy transfer until two objects reach the same temperature.
Heat 热量 flows hot to cold
- Heat (thermal energy 热能) flows from higher to lower temperature.
- It keeps flowing until the temperatures are equal.
Heat (thermal energy) naturally flows from:
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Energy always flows down the temperature difference, from hot to cold, until they are equal.
Thermal equilibrium 热平衡
- When two things reach the same temperature, they are in thermal equilibrium.
- There is then no net flow 净流动 of energy between them.
A thermal (infrared) camera turns temperature into colour: the hot fries glow bright orange, while the cold drink stays dark
At thermal equilibrium there is no net flow of energy between two bodies.
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Equal temperatures mean no net flow — particles still exchange energy, but with no overall transfer.
Two objects in thermal equilibrium are at the same ____.
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Same temperature is exactly the condition for thermal equilibrium.
Match each term to the definition the examiner marks.
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Thermal equilibrium is defined by NO NET transfer, not by no transfer at all. Energy still crosses in both directions; the two flows simply match.
Temperature is not energy
- Temperature decides the direction of heat flow — not how much energy a body holds.
- A tiny spark at $1000\ °\text{C}$ holds far less energy than a warm swimming pool.
Temperature tells you:
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Temperature decides the direction of heat flow; the amount of energy also depends on mass and material.
A hot spark always contains more thermal energy than a warm swimming pool.
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No — the spark is at a higher temperature, but the huge pool holds far more thermal energy overall.
A bucket of warm water contains more internal energy than a red-hot nail, so it is at a higher temperature.
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Temperature is not energy. The bucket holds far more internal energy in total, yet energy flows from the nail to the water, which is what temperature actually decides.
Saying it the exam way
- "Two objects in thermal equilibrium are at the same temperature, so there is no net transfer of thermal energy between them." Both halves score.
- Energy still passes both ways between them — at equal rates, so the net flow is zero.
- A thermometer works by reaching thermal equilibrium with what it touches, which is why it must be left long enough to settle.
Two objects are in thermal equilibrium. Which statements are true? Select all that apply.
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Equilibrium means equal temperature and zero net flow. Energy still passes both ways at equal rates, and the two objects can hold very different amounts of energy.
Worked example: mixing hot and cold water
$0.20\ \text{kg}$ of water at $80\ °\text{C}$ is poured into $0.50\ \text{kg}$ of water at $20\ °\text{C}$ in an insulated cup. Find the final temperature $T$. Take $c = 4200\ \dfrac{\text{J}}{\text{kg}\,\text{K}}$.
- Energy lost by the hot water = energy gained by the cold water, since none escapes.
- $0.20 \times 4200 \times (80 - T) = 0.50 \times 4200 \times (T - 20)$; the $4200$ cancels.
- $16 - 0.20T = 0.50T - 10$, so $0.70T = 26$ and $T = 37\ °\text{C}$.
- Check: the answer lies between $20$ and $80$, and nearer the cold water because there is more of it. Write each $\Delta T$ as a positive number on its own side.
$0.30\ \text{kg}$ of water at $90\ °\text{C}$ is mixed with $0.60\ \text{kg}$ of water at $15\ °\text{C}$ in an insulated container. What is the final temperature, in °C?
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$0.30(90 - T) = 0.60(T - 15)$: $27 - 0.30T = 0.60T - 9$, so $0.90T = 36$ and $T = 40\ °\text{C}$.
200 g of water at 80 C is mixed with 300 g at 20 C. What is the final temperature, in C?
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Energy lost equals energy gained: 200(80 - T) = 300(T - 20), so T = 44 C. The specific heat capacity cancels because both are water.
Worked example: the beaker takes its share
An $810\ \text{W}$ heater warms $120\ \text{g}$ of a liquid in a $42\ \text{g}$ glass beaker from $25\ °\text{C}$ to $80\ °\text{C}$ in $21\ \text{s}$. The specific heat capacity of glass is $0.84\ \dfrac{\text{J}}{\text{g}\,\text{K}}$. Find $c$ for the liquid.
- Energy supplied: $Q = Pt = 810 \times 21 = 17\,000\ \text{J}$.
- Energy into the beaker: $42 \times 0.84 \times 55 = 1940\ \text{J}$ — it warms through the same $55\ \text{K}$.
- Energy into the liquid: $17\,010 - 1940 = 15\,070\ \text{J}$.
- Specific heat capacity: $c = \dfrac{15\,070}{120 \times 55} = 2.3\ \dfrac{\text{J}}{\text{g}\,\text{K}}$.
- Check: the beaker is in thermal equilibrium with the liquid throughout, so it ends at the same temperature and must be counted. Forgetting it gives $2.6$, which looks plausible and is wrong.
Equal temperature is not equal energy: a hot spark and a warm pool. At equilibrium the net flow is zero, not all flow. In any mixing calculation, count every object whose temperature changes — the container included — and use temperature changes in the same units on both sides.
You've got it
- heat flows from higher to lower temperature
- thermal equilibrium: same temperature, no net transfer of thermal energy
- temperature sets the direction of flow, not the amount of energy; mixing problems: energy lost = energy gained, container included