Heat and temperature
Heat is energy that flows from a region of higher temperature to a region of lower temperature. Temperature measures how hot or cold an object is — more precisely, it is related to the average kinetic energy of the particles. Heat and temperature are different: heat is energy (unit joule, J) while temperature is a measure (unit °C or K).
Reaching thermal equilibrium
When a hot object touches a cold object, heat flows from hot to cold. The hot object cools down and the cold object warms up. This continues until both reach the same temperature. At that point the net rate of heat transfer between them is zero — they are in thermal equilibrium.
Key formula / 关键公式
At thermal equilibrium: heat lost by hot object = heat gained by cold object
m₁c₁(θ₁ − θ) = m₂c₂(θ − θ₂)
where θ is the common final temperature. There is no net heat flow once temperatures are equal.
Why thermometers work
A thermometer works on the principle of thermal equilibrium. When placed in contact with a body, heat flows until the thermometer and the body reach the same temperature. The thermometer then reads its own temperature, which now equals the body's temperature.
Worked example / 例题
Hot water at 80 °C is mixed with an equal mass of cold water at 20 °C. Assuming no heat loss and equal specific heat capacities, find the final temperature.
Heat lost = heat gained: mc(80 − θ) = mc(θ − 20).
80 − θ = θ − 20, so 2θ = 100, θ = 50 °C.
Remember / 记住
- Heat always flows from higher to lower temperature.
- Thermal equilibrium means equal temperature, not equal heat energy.
- At equilibrium the net heat transfer is zero, not the temperature.