Question

The sketch shows two identical beakers with different volumes of water at the same temperature. Is the thermal energy content of beaker 1 greater than, less than, or equal to that of beaker \(2 ?\) Explain your reasoning.

Short answer

Beaker with more water has greater thermal energy due to more particles.

Step-by-step solution

Understand the Problem

Identify that we are comparing the thermal energy content of two identical beakers at the same temperature, but with different volumes of water.

Define Thermal Energy

Thermal energy is the total kinetic energy of the particles in a substance. It depends on the temperature and the number of particles (mass or volume) in the system.

Analyze the Relationship

Since both beakers are at the same temperature, the kinetic energy per particle is the same. However, thermal energy also depends on the total number of particles, which is related to the volume of water.

Compare Volumes

If one beaker has more water (a greater volume), it contains more particles. Therefore, it will have a greater thermal energy content, even though the temperature is the same.

Conclusion

The beaker with the greater volume of water has the greater thermal energy because it contains more particles contributing to the total kinetic energy.

Key concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. All matter is made up of tiny particles that are constantly moving, and this movement gives the particles kinetic energy.
In the case of thermal energy, the focus is on the kinetic energy of the particles within a substance. The faster these particles move, the more kinetic energy they have. Therefore, when the temperature of a substance rises, the kinetic energy of its particles increases because they're moving faster.
In terms of thermal energy, it is important to consider not just the speed of the particles (which relates to temperature), but also how many particles there are (which relates to volume and mass). This is why two identical beakers with different volumes of water but at the same temperature can contain different amounts of thermal energy.

Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. It does not measure the total energy present, but rather how much energy each particle has on average.
When we touch an object to find out if it's hot or cold, we're essentially assessing its temperature or the average kinetic energy of its particles.
It's important to note that temperature is not affected by the amount of the substance. This means two different quantities of the same substance at the same temperature still have the same average particle energy, despite possibly having different total energies.

Volume and Mass

Volume and mass are critical factors when determining the total thermal energy of a substance. Volume refers to the amount of space a substance occupies, while mass is the measure of the amount of matter in an object.
For a given temperature, increasing the volume or mass means more particles are present, allowing for more total kinetic energy and thus greater thermal energy.
In our example with the beakers, if one beaker contains more water, regardless of being at the same temperature as the other, it contains more particles and thus more total thermal energy.

• More particles mean more total kinetic energy.
• Larger volume or mass increases total thermal energy without affecting temperature.

This relationship highlights how volume and mass affect energy content without changing the observable temperature.