Video: Identifying the Section of a Temperature-Energy Graph Where the Energy Requirement for Increasing the Temperature Is 4.18 J/g ⋅ °C

At which part of the graph is the energy required to increase the temperature 4.18 J/g ⋅ °C (or 1 cal/g ⋅ °C)? [A] Part A [B] Part B [C] Part C [D] Part D [E] Part E

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Video Transcript

At which part of the graph is the energy required to increase the temperature 4.18 joules per gram per degree Celsius or one calorie per gram per degree Celsius?

This graph is called a heating graph or a heating curve. It shows us the change in temperature and energy as a substance, in this case water, is heated from the solid phase all the way to the gas phase. Each segment corresponds to a different process along the way. In this question, we’re being asked to identify the segment that corresponds to when the energy required to increase the temperature of water is 4.18 joules per gram per degree Celsius.

This question is referring to the specific heat capacity, which is the energy that’s required to raise the temperature of one gram of a substance by one degree Celsius. And this specific heat capacity of 4.18 joules per gram per degree Celsius or one calorie per gram per degree Celsius is the specific heat capacity of liquid water. So, what we’re really being asked in this question is to identify the segment that corresponds to only having liquid water. So to answer this question, let’s thoroughly explore this heating graph to figure out which segment only has liquid water.

You may have noticed that in this heating graph, we have two types of segments. One type is at a slant, where the temperature and energy are both increasing. The other is flat, meaning that the energy is increasing, but the temperature isn’t changing. Temperature is proportional to the average kinetic energy of a substance. So, since the temperature isn’t changing, we know that the kinetic energy isn’t changing during these flat segments.

And since the kinetic energy isn’t changing, the increase in energy during these segments must be due to an increase in potential energy. When changes in potential energy show up in chemistry, it’s often because atoms or molecules are changing their distance with respect to each other, either moving closer or further away. Molecules will change their distance with respect to each other during a phase change, so these segments correspond to a phase change. As we can see from these cartoons, when a substance changes phases, that is, going from a solid to a liquid or a liquid to a gas, the particles move further away from each other. When the substance is a solid, the particles are close together and highly ordered.

When the substance is a liquid, the particles are still close together, but they’re further apart and free to move around each other. And when the substance is a gas, the particles are fully separated and free to move around their container. Separating these molecules is a process that requires energy. So, all of the energy that the substance is absorbing during a phase change is going towards separating these molecules, which is reflected as a change in potential energy as we’ve discussed.

So, now let’s return to our heating curve and identify all of our segments. In segment A, we see that the temperature is increasing. So, this segment doesn’t correspond to a phase change. We’ll also notice that it’s occurring below zero degrees Celsius. Below zero degrees Celsius, only solid water can exist since zero degrees Celsius is the melting point. So, segment A must correspond to a solid heating up.

Segment B is a phase change that’s occurring at zero degrees Celsius, which is the melting point of water. So, B must be melting. After segment B, all of the water has melted. So in segment C, we have liquid water that is increasing in temperature. So, C corresponds to a liquid heating. D corresponds to a phase change that’s occurring at 100 degrees Celsius, which is the boiling point of water. So, D must correspond to water boiling. At the end of segment D, all of the liquid water would have turned into gas. So, segment E corresponds to the gas heating.

To answer this question, we need to figure out which segment corresponds to liquid water. This corresponds to segment C, liquid heating. Though we would have liquid water in segment B and segment D, these segments correspond to a phase change, so we wouldn’t just have liquid water alone. The only segment where we only have liquid water is segment C. So, the part of the graph where the energy required to increase the temperature of the water is 4.18 joules per gram per degree Celsius, which is the specific heat capacity of liquid water, is segment C.

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