According to Einstein, mass and energy are equivalent. So, which weighs more on Earth: a cup of hot coffee or a cup of iced coffee? Why? Do you think the difference is measurable?

Einstein's theory of relativity has transformed our understanding of the universe. One of its most famous results is the equation \( E = mc^2 \). This simple yet profound formula expresses the idea that mass and energy are two sides of the same coin. Here, \(E\) stands for energy, \(m\) is mass, and \(c\) is the speed of light in a vacuum. The equation tells us that a small amount of mass can be converted into a huge amount of energy, as the speed of light squared ( \(c^2\) ) is a very large number. This concept is essential in many fields, from nuclear physics, where it explains the massive energy releases, to everyday scenarios like our coffee example. Understanding that energy adds to mass makes it clear why a cup of hot coffee, which contains more thermal energy, would weigh slightly more than an iced coffee.

Thermal energy is the energy possessed by an object due to the motion of its molecules. It's directly related to the temperature of the object: the higher the temperature, the faster the molecules move, and the more thermal energy they possess. In our coffee example, the hot coffee has a higher temperature than the iced coffee. This means its molecules are moving faster, giving it more thermal energy. One important aspect of thermal energy is that it can be transferred from one object to another. For example, when you heat water on a stove, thermal energy moves from the stove to the water, increasing its temperature and thermal energy. Applying this concept, the hot coffee not only feels warmer; it also has more energy packed within its molecules. This higher thermal energy translates directly to a higher internal energy.

Internal energy is the total energy contained within a system, including both kinetic energy (due to the motion of particles) and potential energy (due to forces between particles). For our hot coffee, the internal energy is higher than that of iced coffee because of its higher thermal energy. When we consider internal energy, we look at all the microscopic activities happening within the liquid. The internal energy increase leads to a slight increase in mass due to the mass-energy equivalence principle. While the actual increase in mass is incredibly tiny — much too small to measure with standard equipment — it's still a fascinating demonstration of how energy and mass are connected. This concept is critical in many scientific fields, from chemistry to thermodynamics, helping us understand how systems store and transfer energy.