The particles that make up matter are always moving, and temperature is a measure of how lively that motion is.
Put hot water and cold water in contact and heat flows from the hot side to the cold side until the two reach the same temperature; then it stops. This state is called thermal equilibrium.
The amount of heat an object gains or loses is found with Q = cmΔT, and by the time equilibrium is reached, the heat lost by the hot water equals the heat gained by the cold water.
The first picture shows how fast the particles move at a given temperature, and the second follows water at 90 °C and 20 °C step by step to equilibrium.
Temperature and moving particles
🔥 The hotter, the livelier
①All matter is made of particles far too small to see
②The particles never stop moving
③The higher the temperature, the faster they move, and temperature measures how lively this motion is
④The picture exaggerates the difference so that you can see it; in fact the average speed of water molecules differs by only about 17 % between 0 °C and 100 °C
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Particles in a box moving at different speeds depending on the temperature
50°C
Heat flow and thermal equilibrium
↔️ Heat flows from hot to cold
①Put hot water and cold water in contact
②heat flows from the hotter side to the cooler side, so the hot water cools and the cold water warms
③Heat flows quickly while the temperature difference is large and more slowly as the difference shrinks
④Once the two are at the same temperature no more heat flows; this state is thermal equilibrium
⑤The two portions of water in the picture have the same mass, so they meet halfway between 90 °C and 20 °C, at 55 °C
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Water at 90 °C and water at 20 °C in contact, exchanging heat until they reach equilibrium at 55 °C
0 steps
Quantity of heat
🌡️ What is a quantity of heat?
①The amount of heat an object gains or loses is called a quantity of heat
②It is measured in cal (calories) or J (joules)
③1 cal is the heat needed to raise 1 g of water by 1 °C
④1 cal is about 4.2 J
Formula for heat
Q = cmΔT
heat = specific heat × mass × temperature change
Summary
Quantity of heat
Q = mcΔt
Q (heat, cal) = c (specific heat, cal/(g·°C)) × m (mass, g) × ΔT (temperature change, °C)
Condition for thermal equilibrium
Qlost = Qgained
If no heat escapes elsewhere, the heat lost by the hot object equals the heat gained by the cold object
Converting units
1 cal ≈ 4.2 J
How calories and joules are related
🎯 Points that often come up
①Temperature measures how lively the motion of particles is
②Heat flows from a hotter object to a cooler one
③Thermal equilibrium is reached when the two objects are at the same temperature and no more heat flows
④Q = cmΔT; the larger the specific heat, the smaller the temperature change for the same heat
⑤Water has a specific heat of 1 cal/(g·°C), larger than most substances
Worked examples and unit test
Example 1
How many calories are needed to raise 100 g of water from 20 °C to 30 °C? (The specific heat of water is 1 cal/(g·°C).)
1
Heat is found with Q = specific heat (c) × mass (m) × temperature change (ΔT).
2
Q = 1 cal/(g·°C) × 100 g × (30 − 20) °C = 1000 cal.
▸ 1000 cal
For 100 g of iron, whose specific heat is about a tenth of water's, roughly 100 cal would give the same 10 °C rise. The larger the specific heat, the more heat it takes to warm something up.
Example 2
Hot water and cold water were left in contact, and after a while their temperatures became equal. In which direction did heat flow, and what is the final state called?
1
Heat always flows from a hotter object to a cooler one.
2
The state in which the two objects are at the same temperature and no more heat flows is called thermal equilibrium.
▸ Heat flowed from the hot water to the cold water, and the final state is thermal equilibrium
As in the picture above, the temperatures close in quickly at first and more slowly as the difference shrinks. At equilibrium the heat lost by the hot water equals the heat gained by the cold water.
Unit Test
Which statement about thermal energy and thermal equilibrium is correct?
①Heat moves on its own from cold to hot
②The higher the temperature, the slower the particles move
③At thermal equilibrium the two objects have the same temperature
④The unit of heat is °C
⑤The larger the specific heat, the faster the temperature changes
▸ ③ At thermal equilibrium the two objects have the same temperature
1
Heat moves from hot to cold (① wrong), and the higher the temperature, the faster the particles move (② wrong).
2
The unit of heat is the calorie or joule (④ wrong), and the larger the specific heat, the more slowly the temperature changes (⑤ wrong); at thermal equilibrium the two objects have the same temperature (③ correct).