Temperature, Heat and Internal Energy

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1Summary 重點摘要

Temperature measures the average kinetic energy of particles; heat is energy transferred because of a temperature difference; internal energy is the total kinetic and potential energy of particles — and Q = mcΔT lets us calculate the heating and cooling around us.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: It all starts with particlesThe microscopic picture is the key to this topic. All matter is made of countless particles that never stop moving randomly: particles in solids vibrate about fixed positions, while particles in liquids and gases can move about freely. Temperature measures the average kinetic energy of this random motion — the higher the temperature, the faster the particles move on average. For example, particles in a cup of hot water move faster on average than those in a cup of cold water, which is why it feels warmer to the touch. Note that temperature describes the average: within the same cup of water, individual particles still move at different speeds.
2. Step 2: Temperature and thermometersTemperature cannot be judged accurately by our senses alone, so we use thermometers. They work on properties that change with temperature: mercury and alcohol thermometers use thermal expansion, while electronic thermometers use electrical resistance. The degree Celsius is the unit used in this topic, with the ice point of water defined as 0°C and the boiling point as 100°C. For example, a clinical thermometer measures a temperature-dependent property of its sensing material and converts it into degrees Celsius; move it from ice water to hot water and the reading rises — a direct reflection of the property changing with temperature.
3. Step 3: Heat is energy in transitHeat and temperature are different concepts, and exams often ask you to distinguish them. Heat is a way energy is transferred: when two objects have a temperature difference, energy flows from the hotter to the colder one, and this transferred energy is heat, measured in joules. For example, put a hot spoon into cold water: the spoon cools down, the water warms up, and energy flows as heat from the spoon to the water. Once both reach the same temperature, there is no net heat flow. Remember: heat flows spontaneously from hot to cold only — we never say an object 'contains heat', only that it absorbs or releases heat.
4. Step 4: The two parts of internal energyInternal energy is the sum of the kinetic and potential energy of all particles in a system — the amount of energy 'inside' the object. The kinetic part comes from the random motion of particles and is tied directly to temperature; the potential part comes from the forces between particles and depends on their separation and arrangement, hence on the state of matter. Mass, temperature and state all affect internal energy. For example, a full kettle of boiling water has more internal energy than a half-full kettle at the same temperature, because it holds twice as many particles; and steam at 100°C has higher internal energy than liquid water at 100°C because its particles have more potential energy.
5. Step 5: Defining specific heat capacityDifferent substances need different amounts of energy for the same temperature rise, so physics defines specific heat capacity c: the energy needed to raise the temperature of 1 kg of a substance by 1°C, in J kg⁻¹ °C⁻¹. Water's specific heat capacity is 4200 J kg⁻¹ °C⁻¹ — exceptionally high among common substances. For example, raising 1 kg of water by 1°C takes 4200 J, while 1 kg of metal usually needs only a few hundred joules; that is why a pan on the same stove soon becomes scorching hot while a pot of water takes a while to boil. The high value also lets oceans moderate the climate of coastal regions.
6. Step 6: Calculating heat with Q = mcΔTThe formula is Q = mcΔT: Q is the heat absorbed or released (joules), m is mass (kg), c is specific heat capacity (J kg⁻¹ °C⁻¹) and ΔT is the temperature change (°C). Keep the units consistent, and remember ΔT is the change — final temperature minus initial temperature. For example, heating 40 kg of water from 20°C to 40°C gives ΔT = 20°C and Q = 40 × 4200 × 20 = 3360000 J, i.e. 3.36 × 10⁶ J; if the water cools from 40°C back to 20°C, it releases exactly the same amount.
7. Step 7: Heating and cooling in daily lifeWith Q = mcΔT, many everyday phenomena can be explained. Water's high specific heat capacity makes it an excellent coolant and heat store: car engines are cooled by water radiators, and hot-water bags hold water rather than sand, because for the same mass, water absorbs or releases more heat with a smaller temperature change. For example, at the beach in summer the sand heats up faster than the sea, so the sand burns your feet while the water feels cool; at night the sea cools slowly too, keeping coastal areas mild. Cities near the sea owe their gentle climate to this high specific heat capacity.

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8Recap Recap

• Temperature measures the average kinetic energy of the random motion of particles; the common unit is the degree Celsius
• Heat is energy transferred from hot to cold due to a temperature difference; internal energy is the sum of the particles' kinetic and potential energy
• Mass, temperature and state of matter all affect internal energy
• Q = mcΔT; the specific heat capacity of water is 4200 J kg⁻¹ °C⁻¹ — keep units consistent
• Water's high specific heat capacity makes it warm up and cool down slowly — it moderates the climate and serves as a coolant