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In everyday speech, heat is used to describe things with a high temperature. In science, heat takes on a more descriptive definition, but retains the same qualities. Heat is the total kinetic energy of a system's component molecules. It is the culmination of the vibrations, rotations, and translations of all the system's molecules. Heat is typically denoted by $Q$, or its differential form, $đQ$, and can be seen to be an inexact differential.

Heat is most often seen in relation to internal energy, $U$, and entropy, $S$, written below. $$dU=đQ+đW$$ $$đQ_{\text{rev}}=TdS$$ $W$ represents work, $T$ represents temperature, and the subscript $\text{rev}$ implies a reversible process.

Temperature is the propensity of a system to transfer heat. What this means is that objects at a higher temperature are more likely to transfer heat away from themselves.

Let's consider an example. Let's say we heat up an iron rod and then place it into room-temperature water. The iron will cool down and the water will warm up. The iron is at a higher temperature than the water. So, it expels a lot of heat. The water is at a low temperature so it expels very little heat. In this scenario, it may seem that only the iron transfers away heat. But a better way to think about it is that the iron transfers heat faster than the water. This means that the net heat transfer is from the iron into the water. When the temperature equilibrates, the iron and the water transfer heat at the same rate. But, this does not imply that the iron and water contain the same amount of heat when their temperatures are equal. It only means that their abilities to expel heat are equal.

Measuring Temperature

It is impossible to measure temperature. You may be thinking, "Well what about thermometers?" Thermometers don't measure temperature. All thermometers measure some variable that is related to temperature. Then, they convert the value to temperature. Consider a mercury-in-glass thermometer. When the temperature rises the mercury expands. This expansion tells us the ambient temperature. The thermometer correlates the volumetric expansion of mercury to the temperature.

Ok, well what about our sense of touch? We can feel when things are hot! Surely we are able to sense temperature? Again, when we are sensing something related to temperature, and not temperature itself. Instead of sensing temperature, we are able to sense net heat transfer. If you want to demonstrate this to yourself, here's an at-home experiment. Prepare a water-ice bath and a warm (not hot) bath of water. Soak one hand in either the warm or the cold bath for a minute, then place both hands into the other bath. Note how the hand that is dry feels a less severe temperature than the hand that was soaked for a minute. This indicates that our ability to sense temperature is actually the ability to sense heat transfer.

(Video) What is Heat? (Thermal Physics)

by Physics Made Easy

In this video, Dr. Reny describes heat. He starts with a description of temperature from a molecular perspective. With that foundation, he describes the transfer of energy between particles. If the particles are at different temperatures, they collide. The collisions transfer energy. We call that heat. So, you'll understand the big picture. Finally, he gives you the official definition of heat. This is a great explanation!

We've begun to study thermodynamics. It's a subset of physical chemistry that investigates the movement of energy. Eventually, we'll apply it to chemical reactions. That's chemical thermodynamics. But, we need to start with classical thermodynamics to build our foundation. Classical thermodynamics relates energy changes to physical changes. For example, we measure shifts in physical properties like volume, pressure, or temperature. But, these shifts happen because of changes in energy. So, we examine the macroscopic properties to understand the microscopic properties.

So far, we've been defining various concepts. We started with internal energy. It was the sum of all the energy stored in a system. Practically, it's the sum of the kinetic and potential energies. Remember, kinetic energy gets stored in all the possible movements of the particles. Atoms and molecules can translate, rotate, and oscillate. Potential energy gets stored within the electrostatic interactions. In chemistry, potential energy comes from bonds and intermolecular forces. So, we developed the foundation for thinking about a system's energy.

Next, we looked at work. We defined it as a transfer of energy. We imagined two scenarios. In the first, a gas moved a piston. In this case, the gas "did work" on the piston. Some of the gas's kinetic energy got transferred into the piston's movement. In the second scenario, we imagined the piston compressing the gas. The piston "did work" on the gas. The piston's movement transfers to the gas. Both of these cases are examples of mechanical work.

Unfortunately, not all work is mechanical. In this lesson, we'll explore non-mechanical transfers of energy.

Temperature: Measuring the Kinetic Energy of Particles

As I said earlier, classical thermodynamics relates energy to physical changes. What measurement relates to the kinetic energy? The temperature! It measures the average kinetic energy of the molecules. Remember, our units for temperature are Kelvin ($K$). The Kelvin scale is an absolute scale. So, zero Kelvin is a unique phenomenon called absolute zero. The premise of absolute zero was that a system would have zero kinetic energy. It's such an important concept that it was included in the third law of thermodynamics. We'll study the third law in more detail once we introduce entropy.

Unfortunately, quantum mechanics teaches us that absolute zero doesn't exist. Do you remember the uncertainty principle? It teaches that we can never know a particle's precise location. What if a particle had zero kinetic energy? It wouldn't move. So, we would know its exact location.

Reaching absolute zero is also limited by any experimental design. Why? Objects transfer energy from warm to cold. So, to reach absolute zero, the lower-temperature entity must already be at absolute zero. It's a circular situation. If you've achieved it, you must have already reached absolute zero. That being said, scientists have produced some minuscule temperatures. The current record is $38pK$. That's pico-Kelvin! In scientific notation, that's $38\times 10^{-12}K$.

Heat: The Microscopic Transfer of Kinetic Energy

Every morning, I make myself a cup of coffee. I fill my kettle with water, place it on the stove, and light the burner. What happens? The water temperature rises until I hit the boiling point. Once my water is boiling, I make myself a delightful pour-over. But what's causing the water's temperature to rise?

First, let's focus on the kettle and water. As the kettle warms, its atoms begin to move faster. They have more kinetic energy. Remember, metals are crystalline solids. So, the kettle's base is composed of many layers of atoms. Remember, they are all metallically bonded. At first, only the particles in the bottom layer gain energy. They begin to vibrate, rotate and translate more. As they do, they collide with the next layer of atoms. The collisions transfer some of the kinetic energy. The process gets repeated up to the topmost layer. But the upper surface is in contact with water. So, the atoms collide with the water molecules. What's the result? They disseminate some of their kinetic energy to the water. The water molecules then collide with other water molecules. Again, they transmit kinetic energy. Temperature measures the average kinetic energy. So, the whole process increases the water temperature. We've heated our water!

Heat is the transfer of energy caused by temperature differences. Eventually, we'll learn to calculate it from our temperature change. But for now, understand that we have two concepts for energy transfer. Work is the energy transferred via mechanical processes. That's why our example was a moving piston. But heat is the energy transfer from non-mechanical processes. In our kettle example, the kettle and water sit there. They don't move. But, there is an energy transfer occurring. That's why we need heat.

Moving from Classical Thermodynamics to Chemical Thermodynamics

As a side note, let's revisit our kettle example. It illustrates how classical thermodynamics transitions into chemical thermodynamics. Above, we ignored the stove. It turns out that I have a gas stove. So, I heat my kettle using a combustion reaction. What if we could determine the energy transferred to the water? It would equal the amount of energy released by the combustion reaction. So, I could find the energy from breaking and reforming the covalent bonds. It turns out that this is what we study in chemical thermodynamics. We'll explore this more when we learn about enthalpy and calorimetry.