1. Thermochromic Ink or Coating: Magic mugs are coated with a special type of ink or paint called thermochromic ink. This ink contains temperature-sensitive pigments that change color in response to temperature fluctuations. These pigments are designed to undergo a reversible chemical change at a specific temperature range.
2. Cold State: When the mug is at room temperature or filled with a cold liquid, the thermochromic pigments in the ink remain in a crystalline form, reflecting certain wavelengths of light and giving the mug its initial color. The design or image printed with the thermochromic ink is typically hidden or faintly visible in this state.
3. Hot State: When a hot beverage like coffee, tea, or hot water is poured into the mug, the temperature of the mug’s surface increases. As the temperature rises within the specific range for the thermochromic pigments, they undergo a phase change from a crystalline form to an amorphous one. This change in structure causes the pigments to absorb and reflect different wavelengths of light, resulting in a different color or a visible design.
4. Reversible Process: The color change is not permanent. As the mug cools down, the pigments revert to their original crystalline form, and the design gradually fades away or returns to its initial state.
5. Design and Imagery: Magic mugs can feature a wide variety of designs, images, patterns, or messages. These designs are created using the thermochromic ink in combination with traditional printing methods.

It’s important to note that the exact temperature at which the color change occurs can vary based on the formulation of the thermochromic ink. Different mugs may have different temperature ranges for the color change. Additionally, the quality of the mug’s coating and the care taken during production can affect the longevity and effectiveness of the color-changing effect.

To maintain the integrity of a magic mug, it’s generally recommended to avoid placing it in a dishwasher or microwave, as the extreme temperatures and harsh conditions in these appliances could potentially damage the thermochromic coating over time.

In essence, the science behind magic mugs involves the manipulation of materials that respond to temperature changes, creating an engaging and visually captivating experience for users as they witness the transformation of the mug’s appearance when exposed to heat.