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THINK ABOUT IT

Imagine that you want two samples of really hot water. You want a large sample to make soup and a smaller sample for a cup of hot cocoa. Will it take the same amount of heat to get both samples to the same temperature?

What is the difference between temperature and heat?

To answer this question, you will explore

EXPLORING THE TOPIC

Particle View of Energy

Consider a sample of water molecules that is heated. What happens to the molecules as more energy is transferred to the sample?

As shown in the illustration (left), atoms and molecules move faster as they are heated. As the movement of the molecules increases, the temperature of the sample goes up.

Now consider two samples of water that contain different numbers of molecules. While the temperatures might be identical, the amount of energy represented by the two samples is not the same. In one sample, you have many quickly moving particles. In the other sample, you have fewer particles, even though they are moving just as quickly. There will be more total energy in the larger sample.

If the water samples in the large pot and the small cup shown in the illustration (bottom left) are both at 85 ºC, you could say that they both have the same “degree of hotness,” or temperature. However, the water in the large pot has a greater total “quantity of hotness” because it is a larger sample. This second concept is referred to as thermal energy. Thermal energy describes the total amount of energy in the particles of a sample. Because the temperature is the same, the gas molecules in both samples are moving with the same average kinetic energy. Because their volumes are different, the two samples have different amounts of thermal energy. So thermal energy is dependent on both the temperature of the sample and on the number of particles in the sample.

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Measuring Heat Transfer

Unfortunately, you cannot measure the thermal energy of a sample of matter directly. A thermometer gives you only an indication of the average kinetic energy. However, changes in thermal energy can be determined using heat transfer.

Imagine that you have three samples of water at different temperatures: a pitcher of water at 80 ºC, a beaker of water at 80 ºC, and a pitcher of water at 50 ºC. Your common sense tells you that the largest 80 ºC sample is the one with the greatest thermal energy. But can that energy be measured or quantified?

You can calculate the amount of thermal energy in each sample by determining how much energy can be transferred from each one. One way to do this is to use the energy in the three samples to warm identical samples of cold water.

Notice that the large sample of water at 50 ºC warms the cold water sample nearly as much as the small sample of water at 80 ºC.

In each case, the mixture reaches thermal equilibrium. That is, the faster moving molecules in the hot sample slow down and the slower moving molecules in the cold sample speed up until they are all moving with the same average kinetic energy. The transfer of energy happens through collisions of the molecules as the samples mix. The temperature of the final mixture depends on the temperatures and the masses of the samples that were mixed.

A UNIT OF ENERGY: THE CALORIE

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Scientists define a unit called a calorie to measure heat transfer. A calorie is the amount of energy needed to raise the temperature of 1 gram of water by 1 Celsius degree. So, this unit of energy is based on heat transfer to or from water. To determine the number of calories needed, you multiply the mass of the water by the temperature increase in Celsius degrees. This can be summarized by the mathematical equation for the heat transfer, q, in terms of the mass of water, m, and the temperature change, ΔT. The uppercase Greek letter delta, Δ, is used to represent a change in quantity.

q = m(1 cal/g · ºC)ΔT

(Remember, 1 g of water is equivalent to 1 mL of water at room temperature.)

So, for example, to raise the temperature of 500 grams of water by 10 ºC, from a temperature of 20 ºC to a temperature of 30 ºC, it would take 5000 calories of energy.

[For a review of this math topic, see MATH Spotlight: Averages on page A-7.]

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LESSON SUMMARY

What is the difference between temperature and heat?

Temperature and heat are different, although they are both related to the motion of atoms and molecules. The temperature of a substance is a measure of the average kinetic energy of its particles. Heat is a process of energy transfer to or from a sample of matter. Thermal energy is a term often used to describe the “energy content” of a sample. The thermal energy of a sample depends on the number of particles in a sample, whereas temperature is the same regardless of the size of the sample. A calorie is a unit of energy. It is defined as the energy required to raise the temperature of 1 g of water by 1 ºC. The energy transferred is referred to as heat.