Temperature, Heat Transfer, and Thermal Equilibrium

The temperature of a substance is a measure of the average kinetic energy of the molecules in the substance, the energy that molecules have from translational motion (moving from point A to point B). One measure of temperature is the degree Fahrenheit (°F). Developed in 1724, the Fahrenheit scale established 0 °F as the temperature of an ice, water, ammonium chloride (NH4Cl) mixture; 32 °F as the temperature of an ice and water mixture; and 96 °F as the human body temperature. Later, the Fahrenheit scale was revised to keep the freezing point of water at 32 °F, but to make the boiling point of water exactly 212 °F, which is why normal human body temperature is now 98.6 °F.

Another measure of temperature is the degree Celsius (°C). Developed in 1742, the Celsius scale established 0 °C as the freezing point of water and 100 °C as the boiling point of water, both at standard atmospheric pressure. In 1954, the Celsius scale was revised based on “absolute zero” and the “triple point” of Vienna Standard Mean Ocean Water (VSMOW). [The triple point is the temperature and pressure at which three states of a substance (in this case, solid, liquid, and gas) can coexist in thermodynamic equilibrium.] This definition fixed the magnitude of one degree Celsius exactly equal to the magnitude of one kelvin. You can convert between the Fahrenheit and Celsius scales using the following formulas:

°F =
9°C
5
32
°C =
5
°F32
9

In 1954, the Kelvin scale was established. The kelvin (K) is the unit of measurement for temperature used by the International System of Units (SI). Unlike the Fahrenheit and Celsius scales, the Kelvin scale is an absolute, thermodynamic temperature scale, which means that there are no negative temperatures on the Kelvin scale. 0 K is absolute zero, the theoretical temperature at which a system has minimal energy. According to classical thermodynamics, the kinetic energy at absolute zero is zero, and all thermal motion ceases. But according to quantum mechanics, a system at absolute zero still possesses quantum mechanical zero-point energy and the kinetic energy of a system can never be zero.

Absolute zero on the Fahrenheit scale is -459.67 °F. Absolute zero on the Celsius scale is -273.15 °C. A nice feature of the Kelvin scale is that it gives you much better sense of the relative magnitude of temperatures. If the temperature rises from 20 °C (68 °F) to 40 °C (104 °F), you may think that the temperature has doubled. But using the Kelvin scale, you will see that the temperature (and therefore, the average kinetic energy of the molecules) has only gone up 6.8% (from 293.15 K to 313.15 K). How is this helpful? Well, according to the ideal gas law (PV = nRT), we would know that the volume of an ideal gas would only increase by 6.8% going from 20 °C to 40 °C… it would not double. You can convert between the Kelvin and Celsius scales using the following formulas:

K =
°C273.15
°C =
K273.15
Mechanisms of heat transfer

Earlier in the unit, I asked you to think about what might cause a molecule to lose energy and speed. And if a molecule does lose energy and speed, where does that energy go? One way for a molecule to lose energy and speed is by colliding with another molecule. When a high-energy molecule collides with a low-energy molecule, energy can be transferred from the high-energy molecule to the low-energy molecule. How much energy is transferred depends on the physics of the collision.

When the fast moving red molecule collides with the slow moving blue molecule, the red molecule loses speed and the blue molecule gains speed. The kinetic energy lost by the red molecule is transferred to the blue molecule. You can see from the graph that the sum of the kinetic energy of the entire system, which includes both molecules, is conserved.

Pool Table Physics

Energy that is transferred from one place to another is called heat. There are three mechanisms through which heat transfer can occur: conduction, convection, and radiation. Conduction occurs when heat is transferred through the physical collision of molecules.

In the simulation above, an ice cube sits between two clouds of water vapor. The water vapor to the left of the ice cube consists of low-energy (cold) water molecules. The water vapor to the right of the ice cube consists of high-energy (hot) water molecules. In phase 1 of the simulation, the water molecules in the ice cube are moving back and forth in the solid state. They are moving slowly, so their average kinetic energy and temperature are low. In phase 2, water molecules in the gas state start colliding with the ice cube from the left. Because the water molecules in the gas state have the same average kinetic energy as the water molecules in the solid state, not much happens. But in phase 3, water molecules in the gas state start colliding with the ice cube from the right, and these water molecules are moving faster and have much more kinetic energy than the water molecules in the ice cube.

Since we are studying heat transfer and not state (phase) changes, we are going to pretend that the water molecules in the gas state stay in the gas state and that the water molecules in the solid state stay in the solid state. When hot water molecules in the gas state collide with cold water molecules in the solid state, energy is transferred and the water molecules in the solid state start moving faster (they heat up). Some of this energy is eventually transferred to the slow moving water molecules in the gas state to the left of the ice cube. If you look closely, you will see that, when some of those slow moving water molecules in the gas state collide with the ice cube, they pick up energy and speed. Energy (or heat) has just been transferred from one location to another (from the right side of the ice cube to the left).

How did this heat transfer happen? Through conduction. A hot water molecule in the gas state collides with a cold water molecule in the solid state. Heat is transferred. The now hot water molecule in the solid state collides with the other cold water molecules in the solid state surrounding it. The heat gets transferred throughout the ice cube through thousands of rapid collisions. When this heat reaches the left side of the ice cube, it gets transferred to a cold water molecule in the gas state through another collision.

The second mechanism through which heat can be transferred is convection. Convection occurs through the bulk movement of molecules. In this case, heat does not get transferred from the right side of the system to the left side of the system through repeated collisions; heat gets transferred because the hot water molecules themselves physically move from the right side of the system to the left. This bulk movement of molecules increases the average kinetic energy (and temperature) of the molecules on the left and decreases the average kinetic energy of the molecules on the right.

In the simulation above, the red water molecules represent hot molecules and the blue water molecules represent cold molecules. All of the red water molecules are on the right side of the box and all of the blue water molecules are on the left side of the box. This means that the temperature in the right side of the box is higher than the temperature in the left side of the box. To demonstrate how heat can transfer purely through convection (the bulk movement of molecules), I have turned off collisions so that, when two molecules run into each other, they will simply pass through each other as though the other molecule is not even there.

Notice how much faster heat is transferred through convection compared to conduction. In a liquid or a gas, where the molecules are free to move around, heat transfer will occur through a combination of both convection and conduction. While the molecules are physically moving around in a liquid or a gas state (convection), they are still colliding and transferring energy to each other (conduction). However, in a solid state, molecules are not free to move around. Because molecules in a solid state are in fixed positions, convection is not possible and all heat transfer must occur through conduction. That is why heat transfer is generally slower through a solid compared to a liquid or a gas.

In radiation, unlike conduction and convection, energy is not carried by molecules or other forms of matter. In radiation, energy is carried by photons (the basic unit of light). That is why radiation can transfer heat through a vacuum. We are not going to spend much time discussing radiation, not because it is not important (there would be no life on Earth if we did not receive energy from the Sun through radiation), but because radiation does not play much of a role in our introduction to chemistry. When atoms and molecules absorb photons, they speed (and heat) up.

Thermal equilibrium

What eventually did happen to the temperature in the box with the red (hot) and blue (cold) water molecules? In the first few seconds of the simulation, heat is clearly transferred from the right side of the box to the left side of the box through convection. This has the effect of heating up the left side of the box… but also cooling down the right side of the box. At some point, the temperatures in both sides of the box become approximately equal. When all parts of (or places in) a system reach the same temperature, then we say that the system has reached thermal equilibrium. This does not mean that heat transfer has stopped. Remember, this is still a dynamic system. The heat transfer in one direction is just being balanced by the heat transfer in the other direction, so the net effect is zero heat transfer and a constant temperature.

You can see the same thing in the ice cube simulation. The hot water molecules to the right of the ice cube are transferring heat to the ice cube. This means that the water vapor to the right of the ice cube is cooling down. After the heat is eventually transferred through conduction to the left side of the ice cube, the water vapor to the left of the ice cube starts to heat up. (Even though the overall heat transfer through the ice cube is from the right to left, you can actually see that heat is being transferred in both directions. A hot water molecule in the solid state will transfer heat to the left if it collides with a cold water molecule on the left, and it will transfer heat to the right if it collides with a cold water molecule on the right. There is a net heat transfer to the left only because there are more cold water molecules on the left then on the right.) A closed system will always move toward thermal equilibrium. There will be a net heat transfer from the hot parts of a system to the cold parts.

Poaching a Chicken Breast

Although closed systems always move toward thermal equilibrium, most systems never get there. Finding a system in thermal equilibrium is actually fairly uncommon. One reason is convection currents. Because warmer air rises while cooler air sinks, convection currents are created in the air. This means that the air along the floor of a room will always be slightly cooler than the air along the ceiling, and the air in this room will never reach thermal equilibrium. (Convection currents are extremely important… convection currents in the atmosphere, the oceans, and the magma below the Earth’s crust drive many of the dynamic processes in the Earth’s system).

Another reason why systems rarely reach thermal equilibrium is because of us pesky living organisms. The cells in our bodies are constantly converting food energy into work and excess heat energy. If one of us is sitting in the room and breathing, our metabolism will try to keep our body at 37 °C (98.6 °F). This means that we will be constantly pumping heat into the room if the room is cooler than 37 °C, and we will be constantly absorbing heat from the room if the room is warmer than 37 °C. (It’s a slightly different story if we are in the room and not breathing!) You will learn more about how food stores energy in chemical bonds and how that energy is released later in this unit.