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Chapter 2: Problem 8

Beaker \(A\) contains water at a temperature of \(15^{\circ} \mathrm{C}\) . Beaker \(\mathrm{B}\) contains water at a temperature of \(37^{\circ} \mathrm{C}\) . Which beaker contains water molecules that have greater average kinetic energy? Explain your answer.

Short Answer

Expert verified
The water in beaker B has a greater average kinetic energy because it is at a higher temperature.

Step by step solution

01

Understand kinetic energy

Kinetic energy is the energy of motion. With regard to molecules in a liquid, more motion translates to more kinetic energy. To make a comparison between the two beakers, you need to apply the principle that higher temperature implies higher kinetic energy.
02

Make the comparison

It's now evident that the water in beaker B, with a temperature of \(37^{\circ} \mathrm{C}\), is hotter than the one in beaker A, which is at \(15^{\circ} \mathrm{C}\). Therefore, based on the principle learned in step 1, beaker B contains water molecules with a higher average kinetic energy because it is at a higher temperature.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Temperature and Kinetic Energy
When we talk about kinetic energy, we're referring to the energy that an object or a particle possesses due to its motion. In the context of molecules in a substance like water, this energy is directly linked to how fast the molecules are moving. The temperature of a substance actually tells us about this molecular movement. Simply put:
  • Higher temperatures mean molecules move faster.
  • Faster moving molecules mean greater kinetic energy.
So, when the temperature of the water in a beaker increases, the average kinetic energy of the water molecules also increases. This is a fundamental concept linking temperature and molecular motion, showing how thermal energy translates into kinetic energy.
Molecular Motion
Molecular motion is the constant, unstoppable dance of molecules. Even at cold temperatures, molecules are in motion. At higher temperatures, however, these movements become more vigorous. This means the average speed and kinetic energy of the molecules are greater:
  • Molecules in hotter water move more rapidly than those in cooler water.
  • This rapid movement is a direct consequence of the heat energy entering the system.
So, when observing water in different beakers as in Beaker A and B, the molecular motion in Beaker B is more dynamic due to its higher temperature of 37掳C compared to 15掳C in Beaker A. This lively motion is what accounts for the difference in kinetic energy.
Temperature Comparison
Comparing temperatures is essential when determining which of two substances contains molecules with greater kinetic energy. In our example with Beaker A and Beaker B:
  • Beaker A is at 15掳C, which is relatively cooler.
  • Beaker B is at 37掳C, noticeably warmer.
Applying the principle that higher temperature equates to higher kinetic energy, we can conclude that the water molecules in Beaker B have more kinetic energy, due to their higher average speed. The higher temperature simply translates into more energy being available for each molecule to move, thus making temperature a powerful indicator of kinetic energy within a substance.

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Most popular questions from this chapter

What does a good hypothesis require?

Perform the following calculations, and express the answers with the correct number of significant figures. $$\begin{array}{l}{\text { a. } 2.145+0.002} \\ {\text { b. }(9.8 \times 8.934)+0.0048} \\ {\text { c. }(172.56 / 43.8)-1.825}\end{array}$$

What is accuracy? What is precision?

Graphing Celsius and Fahrenheit Temperatures The graphing calculator can run a program that makes a graph of a given Fahrenheit temperature (on the \(x\) -axis) and the corresponding Celsius temperature (on the \(y\) -axis). You can use the TRACE button on the calculator to explore this graph and learn more about how the two temperature scales are related. Go to Appendix c. If you are using a TI-83 Plus, you can download the program CELSIUS and run the application as directed. If you are using another calculator, your teacher will provide you with keystrokes and data sets to use. After the graph is displayed, press TRACE. An X-shaped cursor on the graph line indicates a specific point. At the bottom of the screen the values are shown for that point. The one labeled \(\mathrm{X}=\) is the Fahrenheit temperature and the one labeled \(\mathrm{Y}=\) is the Celsius temperature. Use the right and left arrow keys to move the cursor along the graph line to find the answers to these questions. a. What is the Fahrenheit temperature when the Celsius temperature is zero? (This is where the graph line crosses the horizontal \(x\) -axis. What is the significance of this temperature? b. Human internal body temperature averages \(98.6^{\circ} \mathrm{F.}\) What is the corresponding value on the Celsius scale? c. Determine the Fahrenheit temperature in your classroom or outside, as given in a weather report. What is the corresponding Celsius temperature? d. At what temperature are the Celsius and Fahrenheit temperatures the same?

Write the following numbers in scientific notation. a. 0.0006730 b. 50000.0
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