Which of the following demonstrate a positive ΔS? I) Spilling peanuts onto the floor. II) Tidying the bedroom. III) Boiling a liquid. A) I only, B) II only, C) III only, D) I and III, or E) II and III.
ΔS refers to a change in entropy. An entropy has to do with the number of arrangements or configurations that are available to your system given its properties, such as its energy, its volume, or its temperature. The more arrangements that are available to a system, the higher its entropy will be. So far, this definition of entropy is rather abstract. So to make sense of it, let’s compare a substance as a solid to a substance as a gas. Compared to the gas, the solid is very ordered. In the gas, the particles can be arranged however they want to. And it will still be a gas. But in the solid, the particles have to be arranged in a specific way to be a solid.
Because the solid particles have to be arranged in a specific way to be a solid, the gas particles have more arrangements than the solid does. This means that the gas has more entropy than the solid. So now, let’s imagine we have a process where a substance goes from a solid to a gas, such as in the sublimation of CO₂. If we wanted to think about the change in entropy for this process, the gas has more entropy than the solid does because it has more arrangements. So we would expect this process to have a positive change in entropy. This is true in general. If we have a process that goes from a more ordered state to a less order state, we would expect that process to have a positive change in entropy.
And this is because when you have more order, there’s generally fewer arrangements for the particles in the system. But if there’s less order, there’s generally more arrangements for the particle in the system. And more arrangements means higher entropy. If we have the reverse situation where we’re going from a less ordered system to a more ordered system, we would expect the reverse to be true, that that process would have a negative change in entropy. Now that we understand a little bit about entropy, let’s take a look at the processes in the question to determine which of them demonstrate a positive change in entropy.
The first process is spilling peanuts, let’s say from a bowl, onto the floor. Before we spill the peanuts and they’re in the bowl, all the peanuts have to be in one place, in the bowl. But after we spill them, the peanuts can be arranged however they want to on the floor. When we spill the peanuts onto the floor, there’s more arrangements that the peanuts can take because they’re no longer in the bowl. Because the peanuts can have more arrangements after we spill them, there’s more entropy for the peanuts after we spill them than when they’re in the bowl. Because the entropy of the peanuts is higher after we spill them than before, we’d expect spilling the peanuts onto the floor to have a positive change in entropy.
The second process is tidying a bedroom. Before we tidy, stuff can be arranged in the bedroom however it wants to. But after we tidy, everything gets put back into a specific place. Because things can be scattered anywhere in the bedroom before we tidy, there’s more arrangements for our things before we tidy than afterwards. When we put everything back in its spot. Since more arrangements means a higher entropy, there was more entropy before we tidied than afterwards. So we would expect this process to have a negative change in entropy.
Our final process is boiling a liquid, which is where we go from a liquid to a gas. This process is similar to the example of going from a solid to a gas that we looked at earlier. Though a liquid is less ordered than a solid is, it still is more ordered than a gas. Because gas particles can be arranged however they want to in a container where liquid particles have to be somewhat stuck together to be a liquid. The gas has more arrangements of particles than liquid does. Since the gas has more arrangements than the liquid does, which means more entropy. We would expect boiling a liquid to have a positive change in entropy.
We were tasked with identifying which of these processes demonstrated a positive change in entropy. And we determined I, spilling peanuts onto the floor, and III, boiling a liquid. Both demonstrated a positive change in entropy, which matches answer choice D.