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Entropy is a fundamental thermodynamic principle used to describe heat transfer in a system.

The term Entropy is often considered a measure of the “disorder” of a system and the second law of thermodynamics states that if the system is undergoing an irreversible process, then the entropy of the system will always increase.

Think about gas trapped in a container with known volume, pressure and temperature. The gas molecules can have an enormous number of possible configurations. If the container is opened, the gas molecules escape and the number of configurations increases dramatically, essentially approaching infinity. Therefore S, which denotes entropy, definitely increased after opening the container. Thus, ΔS, or the change in entropy,is greater than zero.

Similarly, entropy also increases when hot water is left at room temperature and allowed to cool down. In this video, we will illustrate how to measure the change in entropy of a system during such cooling experiments.

Before learning how to do the experiment and gather data, let’s learn some laws and equations that allow us to calculate rate of temperature change and increase in entropy during cooling experiments.

Newton’s Law of Cooling states that the rate of temperature change of an object is proportional to the difference between its own temperature and the temperature of the surroundings. Using calculus, this relationship can be converted into this equation, where lower case t represents time, Ts denotes temperature of the surroundings, T0 is the initial temperature, and k is a constant that depends on the characteristics of the object and its surroundings.

Using this equation, one can calculate the temperature of a cooling system at any time if all the other variables are known. This equation also shows that temperature is an exponential function of time. Thus, when a hot object, like a glass of hot water, is placed in a cooler environment, its temperature will decrease at an exponential rate until it reaches the temperature of the surroundings.

Now, let’s see how to calculate the change in entropy, or ΔS. Let’s rewind to when the water was hot.

When talking about entropy, we must first define the system. Here, the system is the glass of water plus the air in the room. So the change in entropy of the system, or ΔStotal is a sum of the change in entropies of these individual components. Mathematically, the change in entropy is defined as heat gained or lost, denoted by Q, divided by the temperature.

In this scenario, we know that heat leaves water, thus ΔS for water decreases. On the contrary, the surrounding air gains heat. Therefore, ΔSair increases. From the second law of the thermodynamics, we know the change in entropy of the total system must be positive.

Now let’s see how to conduct an experiment to test these theoretical predictions of Newton’s Law of Cooling and the second law of thermodynamics.

To begin, fill a large beaker with between 500 mL to one L of water. Place the beaker on a hot plate, and heat the water to boiling. Once the water boils, turn off the heating element.

Then, carefully remove the beaker from the hot plate, and place it on the table on top of paper towels. The paper towels will act as insulation between the water and the cool table. Measure the temperature of the water using the thermometer.

Start the stopwatch, and record the temperature of the water every minute for the first 20 minutes.

For the next 20 minutes, record the temperature every 5 minutes.

Stop taking measurements when the water has come close to room temperature. Then, plot the data points in a graph of temperature of the water versus time.

Now let’s analyze the data obtained. The initial temperature of the water was 100 degrees, at 35 minutes the temperature dropped to 50.6, and the surrounding temperature was 28.5 degrees. Plug in these values into Newton’s Law of Cooling, and solve for the cooling constant k.

Now using the calculated value for k, plot the equation as a continuous function. If we lay our measured data points on this chart, we can see that the theoretical and experimental functions follow an almost identical path.

Now let’s talk about entropy. As we know, the total change in entropy, or delta S, is equal to the entropy change for the water plus the room.

The change in entropy equals Q, or the amount of heat transferred from the hot water to the air, divided by T, so the change in entropy can be calculated if Q is known.

Q can be calculated using the relationship between mass, m, specific heat, c, and the change in temperature in Kelvin, delta T. Using the values for water the amount of heat released by the water, Q can be calculated and used to solve for delta S.

Thus, the experimental data shows that the entropy of the total system has increased since heat was transferred from the water to the air molecules in the room. This validates the second law of thermodynamics.

Entropy and the Second Law of Thermodynamics describe a wide range of occurrences in nature and engineering.

A refrigerator is essentially a heat pump, and removes heat from one location at a lower temperature, the heat source, and transfers it to another location, the heat sink, at a higher temperature.

According to the second law, heat cannot spontaneously flow from a colder location to a hotter one. Thus, work, or energy, is required for refrigeration.

A campfire is another example of entropy changes in real life. The solid wood used as fuel burns and turns into a disordered pile of ash. In addition, water molecules and carbon dioxide gas are released.

The atoms in the vapors spread out in an expanding cloud, with infinite disordered arrangements. Thus, the entropy change from burning wood is always positive.

You’ve just watched JoVE’s introduction to entropy and the second law of thermodynamics. You should now understand the basic concept of entropy, Newton’s Law of Cooling, and examples of entropy changes in everyday life. Thanks for watching!