A cup of hot water or a bathtub of warm water?
Which is “hotter”: a cup of water at 80 °C or a bathtub of water at 40 °C? By temperature, the cup. But if you wanted to warm up a cold room, the bathtub could give off far more heat. In everyday speech “hot” does several jobs at once. In chemistry it splits into three different quantities: temperature, heat, and thermal energy.
Energy
Energy is the capacity to do work or to produce heat, and its SI unit is the joule (J). (In physics, you do work on an object when a force moves it some distance in the direction of the force, as when you lift a book from the floor onto a desk.) Energy of motion is kinetic energy动能; energy stored because of position or the interactions between particles is potential energy势能. The chemical energy化学能 stored in a substance is a kind of potential energy that depends on the bonds between its particles and how they are arranged. When a fuel burns, chemical energy becomes heat and light.
Energy can change form and pass from one object to another, but the total stays the same. This is the law of conservation of energy能量守恒定律.
Temperature, thermal energy, and heat
- Temperature温度: as you saw in 2.8.7, temperature measures the average kinetic energy of the particles. It doesn’t depend on how much matter there is: a cup and a bucket of water can both be at 40 °C.
- Thermal energy内能: the total energy of all the particles’ motion. It depends on temperature and also on the amount of matter, so a bathtub at 40 °C has far more thermal energy than a cup at 80 °C. (Chemists also speak of internal energy, the total of all kinetic and potential energy of the particles.)
- Heat热量, symbol q: energy transferred because of a temperature difference. Heat flows on its own from a hotter object to a colder one until both reach the same temperature, called thermal equilibrium热平衡.
At the particle level, when two objects touch, fast-moving particles on the hot side collide with slower particles on the cold side and pass on some of their kinetic energy. The average kinetic energy falls on one side and rises on the other until they are equal.
Heat is energy in transit. An object has thermal energy, but it doesn’t “contain” heat.
System and surroundings
The part of the world you are studying is the system体系; everything else that can exchange energy with it is the surroundings环境. In a neutralization in a beaker, the reacting acid and base are the system, and the water, the beaker, and the air around it are the surroundings.
The sign of q is taken from the system’s point of view: when the system absorbs heat, q > 0; when it releases heat, q < 0. Whatever the system releases, the surroundings absorb.
Units of energy
Chemists usually use joules and kilojoules (1 kJ = 1000 J). An older unit is the calorie (cal), originally the heat needed to warm 1 g of water by 1 °C, now defined as
The “Calorie” on a US nutrition label, with a capital C, is a kilocalorie: 1 Calorie = 1 kcal = 4.184 kJ.
When the two samples of water touch, which way does heat flow, and where does the temperature end up? Predict, then put them in contact. Try 50 g of hot water against 1 kg of warm water, and compare their total thermal energy:
How Chinese textbooks differ
- Chinese middle-school physics uses Q for heat and 内能 (internal energy) for the energy of the particles. Chinese high-school chemistry first meets heat in reactions as 反应热 (heat of reaction) in its elective book 选择性必修 1. US chemistry uses lowercase q from the start, with signs always taken from the system’s point of view.
- Food labels in China give energy directly in kJ, so a Chinese student may never have used Calories. Converting means dividing kJ by 4.184.
Example 1: pouring hot water into a bathtub
A 200 g cup of water at 80 °C is poured into a bathtub holding 100 kg of water at 40 °C. (a) Before mixing, which has the higher temperature, and which has more thermal energy? (b) Which way does heat flow? (c) Is the final temperature closer to 80 °C or to 40 °C?
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Three ideas to keep apart. Temperature measures the average kinetic energy of the particles; thermal energy is the total energy of all of them, so it depends on how much matter there is; heat is energy that moves because of a temperature difference.
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Temperature. The cup is hotter: its water molecules have the higher average kinetic energy.
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Thermal energy. The bathtub holds 100 000 ÷ 200 = 500 times as much water. Its molecules move a little more slowly on average, but their total energy is far larger, so the bathtub has more thermal energy.
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Direction of heat flow. Only temperature matters: heat flows from the 80 °C water to the 40 °C water until they reach the same temperature. Which one has more thermal energy doesn’t matter.
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Final temperature. All the heat the cup loses goes into the bathtub water. Using q = mcΔT from 2.10.3, with water on both sides so c cancels, and calling the final temperature T:
It’s much closer to 40 °C: there is so much bathtub water that it warms only slightly.
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A common mistake. Thinking heat flows from the object with more thermal energy. That would send heat from the bathtub into the cup, the opposite of what happens.
Example 2: Calories on a label
A granola bar’s label says 190 Calories. (a) How many kilojoules is that? (b) How many joules?
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Calories are kilocalories. A food Calorie (capital C) is 1 kcal, so 190 Calories = 190 kcal.
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Convert to kJ. 1 kcal = 4.184 kJ:
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Convert to J. 1 kJ = 1000 J:
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A common mistake. Treating a food Calorie as a small calorie and getting 0.795 kJ, a thousand times too small.
- Ice water is at 0 °C.
0 °C describes how hot or cold it is, which is the average kinetic energy of the particles.
- A radiator transfers 2 × 10⁶ J to a room in an hour.
Energy transferred because of a temperature difference is heat.
- The extra energy a bucket of water at 40 °C has compared with a cup at 40 °C
Same temperature, but more water means more total energy: thermal energy.
- A measure of the average kinetic energy of the particles
The higher the temperature, the faster the particles move on average.
- Flows only when there is a temperature difference, from hot to cold
Heat is energy in transit.
- The total energy of the motion of all the particles in an object
That is the definition of thermal energy.
- What a thermometer reads
A thermometer measures temperature.
- Rubbing your hands together increases their
Rubbing does work on your hands, raising their thermal energy and temperature. No heat comes from a hotter object here.
- What passes from your hand to an ice cube you’re holding
Your hand is warmer than the ice, so energy flows from hand to ice as heat.
Common mistakes
Mistake 1: “A hotter object contains more heat.” Objects don’t contain heat; heat is energy being transferred. A higher temperature means faster particles on average, but thermal energy also depends on how much matter there is.
Mistake 2: “Ice makes your hand cold by sending cold into it.” Energy flows on its own only from hot to cold. Heat flows from your hand into the ice, and your hand feels cold because it is losing energy.
Mistake 3: “At thermal equilibrium, both objects changed temperature by the same amount.” They end at the same temperature, and the heat lost equals the heat gained, but the temperature changes can be very different. In Example 1 the cup cooled by about 40 °C while the bathtub warmed by only about 0.1 °C.
Quick check
Which statement is correct?
Objects don’t contain heat, heat flows on its own only from hot to cold, and every object has thermal energy because its particles always move. Even in ice at 0 °C the molecules vibrate.
How many kilojoules is 1 kcal?
1 cal = 4.184 J, so 1 kcal = 4184 J = 4.184 kJ.
Summary
- Temperature measures the average kinetic energy of the particles. Thermal energy is their total energy and also depends on the amount of matter. Heat is energy transferred because of a temperature difference.
- Heat flows on its own from hot to cold until thermal equilibrium. When the system absorbs heat q > 0, and when it releases heat q < 0.
- Units: 1 kJ = 1000 J, 1 cal = 4.184 J, and 1 Calorie = 1 kcal = 4.184 kJ.
On to AP (for later)
AP topic 6.3 asks you to explain heat transfer and thermal equilibrium with particle collisions: particles on the hotter side have more kinetic energy on average and transfer it in collisions. All of AP Unit 6 takes signs from the system’s point of view, with q positive when the system absorbs heat and negative when it releases heat. ΔH, coming up in this chapter, follows the same rule.