D. Energy and Society · Thermal and Nuclear EnergyTemperature, Thermal Energy and Heat
D2.1 D3.3 D3.7 A1.12About 65 minutes
Learning goals- I can use the kinetic molecular theory to describe what particles are doing in solids, liquids and gases.
- I can explain the difference between temperature, thermal energy and heat.
- I can convert between degrees Celsius and kelvins.
- I can predict the direction of heat flow and describe thermal equilibrium.
Words to know
kinetic molecular theory (KMT)
The model that says all matter is made of tiny particles that are always moving, and that the particles attract each other.
temperature
A measure of the average kinetic energy of the particles in a substance. Measured in °C or K.
thermal energy
The total kinetic and potential energy of all the particles in an object. Measured in joules (J). Also called internal energy.
heat (Q)
Thermal energy that is transferred from a warmer object to a cooler one because of their temperature difference. Measured in joules (J).
absolute zero
The lowest possible temperature, 0 K or about −273 °C, where particles have the least possible kinetic energy.
kelvin (K)
The SI unit of temperature. A change of 1 K is the same size as a change of 1 °C; T(K) = T(°C) + 273.
thermal equilibrium
The state reached when objects in contact are at the same temperature, so there is no net heat flow between them.
Hot sparks, cold hands
A sparkler on Canada Day throws off sparks that are hotter than 1000 °C. Yet a spark landing on a sleeve usually leaves only a tiny mark, while a splash of 100 °C water from the kettle can give a serious burn. How can something hotter do less damage?
The answer is that temperature and thermal energy are not the same thing. A spark is very hot but has almost no mass, so it carries very little energy. The kettle water is cooler but there is much more of it. This lesson sorts out three words people mix up all the time: temperature, thermal energy and heat. Every other lesson in this unit depends on them.
(Safety: sparklers and kettles both cause real burns. Use sparklers only outdoors with a grown-up.)
Remember from Grade 7
In Grade 7 you learned the particle theory of matter: all matter is made of particles that are always moving, and they move faster when they are heated. You also learned that heat flows from warmer to cooler things, and that heat moves by conduction, convection and radiation. This unit turns those ideas into numbers you can calculate with. In the sibling unit Work, Energy and Power you study kinetic and potential energy of whole objects; here we look at the energy of the particles inside objects.
The kinetic molecular theory
Physicists describe matter with the kinetic molecular theory (KMT). It has four main ideas:
- All matter is made of tiny particles (atoms, ions or molecules).
- The particles are in constant random motion. Moving particles have kinetic energy.
- Particles attract each other. The closer they are, the stronger the attraction. Because of these attractions, particles also have potential energy, which depends on how far apart they are.
- Particles collide with each other and with the walls of their container, and energy is passed along in those collisions.
In a solid, particles vibrate around fixed positions and are held tightly. In a liquid, they are still close together but can slide past each other. In a gas, they are far apart and move freely in straight lines between collisions.
Temperature, thermal energy and heat
- Temperature tells you how fast the particles are moving on average. More precisely, it measures the average kinetic energy of the particles. A thermometer measures temperature.
- Thermal energy is the total energy of all the particles: all their kinetic energy plus all their potential energy. It depends on the temperature and on how much matter there is. It is measured in joules (J).
- Heat is thermal energy on the move. It is the energy transferred from a warmer object to a cooler one because of their temperature difference. We use the symbol Q and the unit joules.
So an object has thermal energy and has a temperature, but it does not "have" heat. Heat is something that flows. Physicists say "heat flowed from the tea into the mug", not "the tea contains a lot of heat".
The Kelvin scale
If you keep cooling something, its particles slow down more and more. There is a lowest possible temperature, called absolute zero, where the particles have the least kinetic energy they can have. Absolute zero is about −273 °C (more precisely −273.15 °C).
The Kelvin scale starts at absolute zero. Its unit is the kelvin (K); we write "300 K", not "300 °K". One kelvin is the same size as one Celsius degree, so:
T(K) = T(°C) + 273 and T(°C) = T(K) − 273
Because the steps are the same size, a temperature change is the same number in both units: warming by 15 °C is warming by 15 K. In this unit we mostly use °C, but you will need kelvins in SPH4U and in chemistry (SCH3U gas laws).
Worked exampleExample 1: Converting temperatures
(a) A January morning in Winnipeg is −30 °C. What is this in kelvins? (b) Liquid nitrogen boils at 77 K. What is this in °C? (c) A pot of soup warms from 18 °C to 93 °C. Find the temperature change in °C and in K.
- (a) T(K) = T(°C) + 273 = −30 + 273 = 243 K.
- (b) T(°C) = T(K) − 273 = 77 − 273 = −196 °C.
- (c) ΔT = T(final) − T(initial) = 93 °C − 18 °C = 75 °C.
- In kelvins: 366 K − 291 K = 75 K. A change is the same in both units because the step sizes are equal.
243 K; −196 °C; ΔT = 75 °C = 75 K.
Which way does heat flow?
Put a hot object in contact with a cold one. The faster particles of the hot object bump into the slower particles of the cold object and pass on some of their kinetic energy. Overall, energy moves from the higher-temperature object to the lower-temperature object. The hot object cools down and the cold one warms up.
This continues until both are at the same temperature. Then they are in thermal equilibrium. Particles still collide, but energy moves equally both ways, so there is no net heat flow.
Heat always flows from higher temperature to lower temperature on its own, never the other way. (Notice: it depends on temperature, not on which object has more thermal energy. A hot mug placed in a cool lake gives heat to the lake, even though the lake has far more thermal energy.) To push heat from cold to hot, you need a machine that uses energy, such as a refrigerator or a heat pump. You will see how they work in the lesson Heat Pumps, Refrigerators and Thermal Technologies.
Worked exampleExample 2: Temperature or thermal energy?
A 200 g cup of hot chocolate is at 70 °C. A 50 kg bathtub of water is at 40 °C. (a) Which has the higher temperature? (b) Which has more thermal energy? (c) If the cup is placed floating in the bathtub, which way does heat flow?
- (a) Temperature is the average kinetic energy of the particles. The hot chocolate is at 70 °C, so it has the higher temperature.
- (b) Thermal energy is the total energy of all the particles. The bathtub has 250 times as much mass, so it has far more particles and far more thermal energy, even at a lower temperature.
- (c) Heat flows from higher temperature to lower temperature: from the hot chocolate into the bath water, even though the bath has more thermal energy. The hot chocolate cools a lot; the bath warms very slightly.
The hot chocolate has the higher temperature; the bathtub has more thermal energy; heat flows from the cup into the bath.
Just for funThe coldest temperature ever officially recorded in Canada was −63.0 °C, at Snag, Yukon, in February 1947. That sounds brutal, but it is still about 210 K, so the particles in Snag's air were still zipping around. Physicists would call that "warm".
Hands-on activityFast and slow particles in your kitchen
You need: two clear glasses, cold tap water, hot tap water (a grown-up should handle it; hot tap water can scald), food colouring, a kitchen thermometer if you have one.
- Fill one glass with cold tap water and one with hot tap water, the same amount in each. Let them sit still for 1 minute. If you have a thermometer, measure and record each temperature.
- At the same moment, add one drop of food colouring to the middle of each glass. Do not stir.
- Watch for 2 minutes. Sketch what each glass looks like after 30 s, 1 min and 2 min.
- Explain your observations using the kinetic molecular theory. Use the words temperature, average kinetic energy and random motion.
- Leave both glasses on the counter for an hour, then measure the temperatures again. Which glass changed temperature more? Where did its thermal energy go?
What to look for: the colour spreads much faster in the hot water, because its particles have a higher average kinetic energy and bump the dye particles around more. After an hour both glasses approach room temperature: the hot water lost thermal energy to the air and counter (heat flowed out), and the cold water gained some.
Your turn
1Convert 25 °C to kelvins.
3A sidewalk warms from −12 °C to 4 °C. What is ΔT in °C and in K?
ΔT = 4 − (−12) = 16 °C, which is also 16 K.
4In your own words, what does temperature measure?
The average kinetic energy of the particles in a substance (how fast they move on average).
5Why is it wrong to say "this soup contains a lot of heat"?
Heat is energy being transferred because of a temperature difference. The soup has thermal energy; heat is what flows out of it into cooler surroundings.
6A 1 L pot of water and a 5 L pot of water are both at 60 °C. Compare their temperatures and their thermal energies.
They have the same temperature (same average kinetic energy), but the 5 L pot has about 5 times the thermal energy because it has 5 times as many particles.
7An ice cube is dropped into a glass of juice at 15 °C. Which way does heat flow, and when does it stop?
Heat flows from the juice into the ice. The net flow stops when everything reaches the same temperature (thermal equilibrium).
More practice: warm-up
1What is absolute zero in °C (to the nearest degree)?
2What is the SI unit of heat?
3In which state do particles vibrate around fixed positions?
4Convert 0 K to °C and 0 °C to K.
0 K = −273 °C; 0 °C = 273 K.
5True or false: heat flows on its own from a cold object to a hot object.
False. On its own, heat always flows from higher temperature to lower temperature.
More practice: on your own
1Oxygen boils at −183 °C. Express this in kelvins.
2Which has more thermal energy: a 5 g sparkler spark at 1200 °C or a 2 kg pot of water at 90 °C? Explain.
The pot of water. Thermal energy depends on the amount of matter as well as temperature. The spark is very hot but has a tiny mass, so its total energy is far smaller.
3Use the KMT to explain why a balloon left in a hot car gets tighter.
Higher temperature means the gas particles move faster on average. They hit the inside of the balloon harder and more often, pushing the rubber outward.
4Two blocks of copper touch. Block A is at 300 K and block B is at 40 °C. Which way does heat flow?
Convert: 40 °C = 313 K. B (313 K) is warmer than A (300 K), so heat flows from B to A.
5A student says, "At thermal equilibrium the particles stop colliding." Correct the statement.
Particles keep colliding. At equilibrium, energy is passed equally in both directions, so there is no net heat flow.
Challenge
1Why is it impossible to have a temperature of −300 °C?
−300 °C would be −27 K, below absolute zero. At 0 K particles already have the least possible kinetic energy, so they cannot slow down any further. No temperature below absolute zero exists.
2A large iceberg at −5 °C and a small cup of tea at 60 °C. Explain, using KMT, which has more thermal energy and which way heat would flow if the tea were poured onto the iceberg.
The iceberg has enormously more particles, so its total kinetic plus potential energy (thermal energy) is far larger. But heat flow depends on temperature: the tea's particles have a higher average kinetic energy, so heat flows from the tea into the ice. The tea cools and some ice warms or melts.
3Kelvin temperatures are proportional to average kinetic energy. If a gas is heated from 27 °C to 327 °C, by what factor does the average kinetic energy of its particles increase?
Convert: 27 °C = 300 K and 327 °C = 600 K. The Kelvin temperature doubles, so the average kinetic energy doubles (factor of 2). (It is not 327 ÷ 27 ≈ 12; only Kelvin values can be used for ratios.)
Quiz
1. Which quantity is a measure of the average kinetic energy of the particles in a substance?
2. What is 310 K in degrees Celsius?
3. Which statement about heat is correct?
4. A swimming pool at 26 °C and a cup of coffee at 75 °C. Which is true?
5. A metal spoon at 20 °C is placed in soup at 80 °C. What happens until thermal equilibrium?
6. A sample warms from 250 K to 290 K. What is the temperature change in °C?
Big idea: this lesson sets up the vocabulary for the whole unit (expectation D2.1) and the kinetic molecular theory (D3.7). Students must keep temperature (average kinetic energy), thermal energy (total energy of the particles) and heat (energy transferred) separate.
How to help: Ask your teen to explain everyday situations aloud: why the big pot of soup stays hot longer than a small bowl; why you feel cold getting out of a lake on a hot day. Listen for "heat flows from hot to cold" and "more mass means more thermal energy".
Common difficulties:
- Saying an object "contains heat". Gently correct to "has thermal energy".
- Thinking cold flows. Only heat (energy) flows, always from higher to lower temperature.
- Forgetting to add 273 when converting to kelvins, or adding it to a temperature change. A change of 10 °C is a change of 10 K.
- Using ratios of Celsius temperatures. Only Kelvin temperatures can be compared as ratios (Challenge 3).
Safety: the activity uses hot tap water; a grown-up should pour it.