# Temperature and Thermal Properties of Matter

Physics I · Principles of Waves, Fluids and Thermodynamics · https://tryals.app/learn/physics-i/temperature-and-thermal-properties-of-matter

## Temperature & Energy

Temperature is not a substance, but a census: the average kinetic energy of microscopic molecules. **Temperature** measures this average kinetic energy, while **heat** is energy transferred strictly due to a temperature difference.

**Common pitfall:** Temperature and heat are distinct. A 1000 degree sparkler holds far less thermal energy than a 40 degree bathtub because heat depends on total molecular count.

**Temperature scales** convert via:

$T_K = T_C + 273.15$

$T_F = \frac{9}{5}T_C + 32$

**Thermal expansion** causes materials to grow when heated, tracked by linear and volume formulas:

$\Delta L = \alpha L_0 \Delta T$

$\Delta V = \beta V_0 \Delta T$

Here, $\beta \approx 3\alpha$, representing the expansion coefficients.

## Heat & Phase Changes

**Heat capacity** determines energy needed to shift temperature via $Q = mc\Delta T$.

| Substance | $c$ (J/(kg K)) |
| --- | --- |
| Water | $4186$ |
| Aluminium | $900$ |
| Copper | $385$ |
| Iron | $449$ |

**Phase changes** occur at constant temperature using $Q = mL$, where $L$ is **latent heat** of fusion or vaporisation.

**Calorimetry** in isolated systems dictates heat lost equals heat gained:

$\sum Q_i = 0$

$m_1 c_1(T_f - T_1) + m_2 c_2(T_f - T_2) = 0$

**Tip:** Always check for phase changes before applying $Q = mc\Delta T$. At melting or boiling points, account for latent heat first.

## Practice questions

5 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. A metal washer (a disk with a hole) is heated uniformly. What happens to the **hole**?

A. It depends on the metal’s expansion coefficient
B. It stays the same size, holes are not made of metal
C. It shrinks as the metal expands into it
D. It expands, right along with the metal

**Answer:** D. It expands, right along with the metal

**Why:** Uniform expansion is a uniform rescaling of **all** distances, holes included. That is why a stuck metal lid loosens under hot water: the lid’s opening genuinely widens.

Page: https://tryals.app/practice/physics-i/temperature-and-thermal-properties-of-matter/a-metal-washer-a-disk-with-a-hole-is-heated-uniformly-what-happens

### 2. A 30 m steel bridge span heats from −10 °C in winter to 40 °C in summer ($\alpha \approx 1.2\times10^{-5}$ per °C). Estimate how much longer it gets, in **centimetres**.

**Answer:** 1.8 (within ±0.5)

**Why:** About 1.8 cm, small in fraction, unstoppable in force. Expansion joints (those toothed gaps you drive over) exist to give these centimetres somewhere to go.

Page: https://tryals.app/practice/physics-i/temperature-and-thermal-properties-of-matter/a-30-m-steel-bridge-span-heats-from-10-c-in-winter-to-40-c-in

### 3. Two objects at the same temperature can hold very different amounts of thermal energy. Why does temperature not measure the total?

A. The average kinetic energy per particle, not the total
B. The total thermal energy divided by the volume
C. The rate at which an object loses heat to its surroundings
D. The total number of particles moving above a threshold speed

**Answer:** A. The average kinetic energy per particle, not the total

**Why:** Temperature is intensive and thermal energy is extensive. That is why a spark at 1000 °C is harmless and a bath at 60 °C is not, and why heat flow follows temperature, not energy content.

Page: https://tryals.app/practice/physics-i/temperature-and-thermal-properties-of-matter/two-objects-at-the-same-temperature-can-hold-very-different-amounts

### 4. Which statements about thermal expansion are correct?

A. Solids expand when heated
B. Bridges require expansion joints to accommodate thermal changes
C. Water contracts when cooled from 4°C to 0°C (anomalous expansion)
D. Thermal expansion is identical for all materials

**Answer:** A. Solids expand when heated; B. Bridges require expansion joints to accommodate thermal changes; C. Water contracts when cooled from 4°C to 0°C (anomalous expansion)

**Why:** Most materials expand on heating; water is anomalous near 4°C. Each material has its own expansion coefficient.

Page: https://tryals.app/practice/physics-i/temperature-and-thermal-properties-of-matter/which-statements-about-thermal-expansion-are-correct

### 5. Order these milestones in the history of thermometry and thermal physics.

**Answer:**

1. Galileo invents the first thermoscope
2. Fahrenheit introduces his temperature scale
3. Celsius proposes the centigrade scale
4. Kelvin defines absolute temperature scale
5. International Temperature Scale (ITS-90) adopted

**Why:** Galileo (c. 1592), Fahrenheit (1714), Celsius (1742), Kelvin (1848), ITS-90 (1990).

Page: https://tryals.app/practice/physics-i/temperature-and-thermal-properties-of-matter/order-these-milestones-in-the-history-of-thermometry-and-thermal