Thermal Energy Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Thermal Energy.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The total kinetic energy of all particles in an object due to their random motion.

The energy of jiggling atoms and molecules—what we experience as temperature.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Temperature measures average kinetic energy; thermal energy is the total.

Common stuck point: Heat is energy transfer due to temperature difference; thermal energy is what's stored.

Worked Examples

Example 1

easy
How much thermal energy is needed to heat 2 \text{ kg} of water from 20°\text{C} to 80°\text{C}? The specific heat capacity of water is c = 4186 \text{ J/(kg·°C)}.

Solution

  1. 1
    Use the thermal energy formula: Q = mc\Delta T.
  2. 2
    Temperature change: \Delta T = 80 - 20 = 60°\text{C}.
  3. 3
    Q = 2 \times 4186 \times 60 = 502{,}320 \text{ J} \approx 502 \text{ kJ}

Answer

Q \approx 502 \text{ kJ}
Thermal energy (heat) required to change an object's temperature depends on its mass, specific heat capacity, and the temperature change. Water has a very high specific heat, requiring lots of energy to heat.

Example 2

medium
A 0.5 \text{ kg} iron block (c = 450 \text{ J/(kg·°C)}) at 200°\text{C} is dropped into 2 \text{ kg} of water (c = 4186 \text{ J/(kg·°C)}) at 20°\text{C}. What is the final equilibrium temperature?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A 3 \text{ kg} aluminum block (c = 900 \text{ J/(kg·°C)}) absorbs 54{,}000 \text{ J} of thermal energy. What is the temperature increase?

Example 2

hard
A 1200 \text{ kg} car traveling at 30 \text{ m/s} brakes to a stop. If all kinetic energy is converted to thermal energy in the brakes (4 \text{ kg} of steel, c = 500 \text{ J/(kg·°C)}), by how much do the brakes heat up?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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