TL;DR:
Temperature measures how energetic the particles are on average. Heat is energy transferred because of a temperature difference.
The energy to change a temperature is
Q = mcΔT. Warming 1 kg of water by 10 °C takes about 41.9 kJ.Water has a large specific heat, which is why coastal climates are milder than inland ones.
A spark from a fireplace can be far hotter than a mug of tea, yet it does not hurt much when it lands on your hand, while the tea can scald you. Temperature alone does not tell you how much energy is around. That is the difference between temperature and heat.
Two different quantities
Temperature tells you how fast the particles in a material move about, on average. A higher temperature means more average kinetic energy per particle. It does not depend on how much material you have.
Heat is energy that moves from one object to another because of a temperature difference. It goes from hot to cold, and it stops flowing when the two reach the same temperature. Heat is measured in joules, not degrees. Things do not contain heat, they contain internal (thermal) energy, and heat is the transfer.
A bathtub of lukewarm water holds far more thermal energy than a cup of boiling water, even though its temperature is lower. More particles means more total energy.
How much energy a temperature change takes
Materials differ in how much energy they need to warm up. The specific heat capacity c is the energy needed to raise 1 kg of the material by 1 °C (or 1 K, the step size is the same). The formula is Q = mcΔT.
Q is the heat transferred, in joules.
m is the mass, in kilograms.
c is the specific heat, in J/(kg·°C). For liquid water it is about 4186, often rounded to 4190.
ΔT is the change in temperature, final minus initial.
Worked example: warming 1 kg of water by 10 °C
Write the formula:
Q = mcΔT.Substitute:
Q = 1 × 4186 × 10.Multiply:
Q = 41,860 J, which is about 41.9 kJ.Units:
kg × J/(kg·°C) × °C = J.
How long would this take? Say an electric kettle delivers 1000 W (1000 J each second) with no loss. Then 41,860 J ÷ 1000 J/s ≈ 42 s. Real kettles take a little longer because some energy warms the kettle and the air.
Compare copper, with c about 385 J/(kg·°C). For 1 kg and the same 10 °C: 1 × 385 × 10 = 3850 J. That is 41,860 ÷ 3850 ≈ 10.9 times less energy than water needs. Water soaks up a lot of energy for each degree, and metal does not.
Mixing gives a neat check. Mix 1 kg of water at 80 °C with 1 kg at 20 °C. The hot water gives up 1 × 4186 × (80 − T) and the cold takes in 1 × 4186 × (T − 20). Setting them equal gives 80 − T = T − 20, so T = 50 °C. Same mass, same material, so the temperature lands halfway.
Hot water scalds: Water at kettle temperature can cause serious burns quickly. Do not carry it in a rush, keep the spout pointed away from you and keep young children away. Handle hot pots with proper holders.
Why coastal climates are mild
Land and sea get the same sunshine, but water has a large specific heat and also mixes, spreading energy through a deep layer. It takes a lot of energy to warm the sea by a degree, and it gives a lot back when it cools by a degree.
So a place near a large body of water sees smaller swings between day and night and between summer and winter than a place far inland. Sea breezes also move that moderated air onto the land. The ocean acts like a huge thermal buffer.
How to check your answer
Units. Mass in kg, c in J/(kg·°C), answer in joules. Convert grams to kilograms.
Sign. Heating gives positive Q, cooling gives negative Q.
Scale. Doubling the mass or the temperature change doubles Q.
Sense check. A material with a large c should take longer to heat under the same power.
Mistakes that cost marks
Using the final temperature instead of the change
ΔT.Saying a hot object contains heat. It has thermal energy, and heat is the transfer.
Using grams with a specific heat per kilogram.
Using
Q = mcΔTacross a phase change, where energy goes into melting or boiling and the temperature stays put.Thinking temperature and heat are the same thing, or that cold flows into a warm object. Heat flows out of the warm one.
Where you will use it next
The next step is phase changes and heat engines. Energy bookkeeping also shows up in nuclear physics, such as half-life and radioactive decay, where the energy released in decay warms the surroundings. If you want a refresher on how floating and density interact with temperature, see buoyancy.
Frequently asked questions
Can two objects have the same temperature but hold different amounts of thermal energy?
Yes. A larger object, or a material with a larger specific heat, holds more energy at the same temperature.
Why does metal feel colder than wood at the same room temperature?
Metal conducts heat away from your hand faster, so your skin cools more quickly. The temperatures are actually equal.
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