Problem 28 - An Introduction to Physical Science

Question

Compare Two glasses of water are poured into a pitcher. If the temperature of the water in both glasses was the same before and after they were mixed, describe how the thermal energy of the water in the pitcher compares to the water in the glasses.

Step-by-Step Solution

Answer

The thermal energy in the pitcher is twice the thermal energy of each individual glass.

Step 1: Understand the concept of thermal energy

Thermal energy is the total kinetic energy of the particles in a substance due to their random motion. When two bodies of water at the same temperature are combined, their temperatures remain the same, but their total thermal energy is the sum of the thermal energies of each individual body of water.

Step 2: Determine the initial thermal energy of each glass of water

Assume each glass of water has a certain amount of thermal energy. Let's denote the thermal energy of one glass of water as E. Therefore, the thermal energy of each glass is equal to E before mixing.

Step 3: Calculate the total thermal energy in the pitcher

When the two glasses of water are poured into the pitcher, the total thermal energy in the pitcher is the sum of the individual thermal energies of the two glasses of water. Since each glass of water has thermal energy E, the total thermal energy in the pitcher is 2E.

Step 4: Describe the thermal energy comparison

The thermal energy of the water in the pitcher (2E) is twice the thermal energy of the water in each individual glass (E). This is because thermal energy is additive for masses of water that are combined.

Key Concepts

Thermal Energy

Thermal energy is a measure of the total kinetic energy of particles in a substance. It arises from the random motions of atoms and molecules within the substance. When you combine two bodies of water at the same temperature, their thermal energies add up.

In simple terms, thermal energy depends on:

• The number of particles
• How fast these particles are moving

So, if you pour two glasses of water into a pitcher, each with the same temperature, then the pitcher will have twice the thermal energy of one glass. That is to say, the thermal energy of the pitcher is the sum of the thermal energies of the two glasses.

Kinetic Energy

Kinetic energy is the energy of motion. Each particle in a substance like water has kinetic energy due to its movement. The more the particles move, the higher their kinetic energy.

When we talk about the thermal energy of water, we are referring to the collective kinetic energy of all the water molecules moving randomly. Even though thermal energy and kinetic energy are related, they are not the same. Thermal energy includes the total kinetic energy of all particles in the system.

Consider two glasses of water at the same temperature; the particles in both are moving at similar speeds. When combined, although the temperature remains the same, the number of moving particles—and therefore the total kinetic energy—increases. That's why the total thermal energy doubles when the two bodies of water are mixed in the pitcher.

Temperature

Temperature measures the average kinetic energy of the particles in a substance. It tells us how hot or cold an object is. Although total thermal energy increases when you mix two bodies of water, the temperature remains the same if the initial temperatures are identical.

Here's a simple way to remember the difference:

• Temperature tells us about the average motion of particles
• Thermal energy is about the total motion of all the particles combined

Therefore, when the water from two glasses with the same temperature is poured into a pitcher, the temperature doesn't change. The average kinetic energy of the particles remains constant, but the total kinetic energy—and thus the thermal energy—increases.