7.5 Relationship Between the Motion of Particles and Temperature

Have you ever noticed that a cup of hot tea has more energy than a cup of cold tea, even though they contain the same amount of liquid? The difference lies in the motion of their particles. The temperature of a substance is directly related to the average kinetic energy of its particles. Understanding this relationship is fundamental to understanding heat, temperature, and changes of state.

Definition

Temperature is the measure of the degree of hotness or coldness of a substance. It is directly proportional to the average kinetic energy of the particles (atoms or molecules) in the substance.

The relationship can be stated as: T ∝ Average KE of particles

Main Idea

The main idea is that temperature is a measure of the average kinetic energy of the particles in a substance. When a substance is heated, its particles move faster, increasing their kinetic energy, and the temperature rises. When a substance is cooled, its particles move slower, decreasing their kinetic energy, and the temperature falls. At absolute zero (0 K or -273.15°C), the particles have the minimum possible kinetic energy (theoretically zero).

Core Concept

The Relationship The text states: "The temperature of a substance is the measure of its hotness or coldness, and the temperature of a substance is directly proportional to the average K.E. of its particles."

T ∝ Average KE

Heating and Cooling The text states: "When we heat a substance (at room temperature), the speed and kinetic energy of its particles increase. That is why the temperature of the substance will also increase. Conversely, when we remove heat from a substance (for example, by placing hot water on ice or in a refrigerator), the speed and kinetic energy of the particles will become slower and slower. Therefore, the temperature of the substance will also decrease."

• Heating: Particles move faster → kinetic energy increases → temperature rises.
• Cooling: Particles move slower → kinetic energy decreases → temperature falls.

Absolute Zero The text states: "If we keep on removing the heat energy from a substance, its particles will keep on slowing down and hence keep on losing kinetic energy. By doing so, a stage will come when molecules will no longer be moving and they have least or no kinetic energy. Particles cannot collide with each other or with the container, therefore they cannot exert pressure (P=0 Pa). At this point, temperature of the substance is called absolute zero."

• Absolute zero: The lowest possible temperature, where particles have the least possible kinetic energy.
• Value: 0 K on the Kelvin scale, or -273.15^°C on the Celsius scale.
• At absolute zero: Particle motion is minimal (theoretically zero in classical physics), and pressure is zero.

The Graph The text includes a graph (Figure 7.8) showing the relationship between temperature and kinetic energy. The graph is a straight line, confirming that temperature is directly proportional to the average kinetic energy of the particles.

The text also includes a graph (Figure 7.8b) showing the relationship between temperature and pressure. The pressure of a gas is also proportional to temperature (at constant volume), and the graph shows that pressure reaches zero at -273^°C, confirming absolute zero.

Detailed Explanation

The relationship between particle motion and temperature is a cornerstone of thermodynamics and statistical mechanics.

Kinetic Theory of Matter The kinetic theory of matter states that all matter is made up of particles (atoms or molecules) that are in constant motion. The temperature of a substance is a measure of the average kinetic energy of these particles.

• Solids: Particles vibrate about fixed positions. Higher temperature means greater vibrational kinetic energy.
• Liquids: Particles move around each other. Higher temperature means greater translational and rotational kinetic energy.
• Gases: Particles move freely at high speeds. Higher temperature means greater translational kinetic energy.

Average Kinetic Energy The average kinetic energy of particles in a gas is given by: Average KE = 32kT where: - k is the Boltzmann constant (1.38 × 10^-23 J/K). - T is the absolute temperature in Kelvin.

This equation shows that the average kinetic energy is directly proportional to the absolute temperature. If you double the temperature (in Kelvin), you double the average kinetic energy of the particles.

Absolute Zero Absolute zero is the lowest possible temperature, at which particles have the minimum possible kinetic energy. In classical physics, particles would have zero kinetic energy at absolute zero. However, quantum mechanics tells us that particles still have some residual motion (zero-point energy) even at absolute zero.

• Particle motion is minimal.
• Pressure is zero (for an ideal gas).
• The substance is in its lowest energy state.

• Thermometers: Thermometers work because the physical properties of materials (e.g., volume expansion, electrical resistance) change with temperature, which is a measure of the average kinetic energy of their particles.
• Changes of State: When a substance is heated, the increased kinetic energy of its particles can overcome the interparticle forces, causing a change of state (e.g., melting, boiling).
• Heat Transfer: Heat flows from a region of higher temperature to a region of lower temperature, transferring kinetic energy from faster-moving particles to slower-moving ones.

Intermediate Level

In physics, temperature is defined as the measure of the average kinetic energy of the particles in a substance. This is a fundamental concept in the kinetic theory of gases. The relationship is directly proportional: if you increase the temperature, the average kinetic energy of the particles increases, and vice versa.

For an ideal gas, the average kinetic energy is given by KE_avg = 32kT, where k is the Boltzmann constant and T is the absolute temperature in Kelvin. This equation shows that temperature is a measure of the average kinetic energy of the particles, not the total kinetic energy.

At absolute zero (0 K or -273.15^°C), the particles have the minimum possible kinetic energy. In classical physics, this would be zero, but quantum mechanics shows that there is still some residual motion (zero-point energy).

The relationship between temperature and particle motion explains many phenomena, including thermal expansion, changes of state, and heat transfer. When a substance is heated, its particles move faster and take up more space (thermal expansion). When it is cooled, the particles move slower and take up less space (contraction).

Important Points

• - Temperature: Measure of the average kinetic energy of particles.
• - Directly proportional: T ∝ Average KE.
• - Heating: Particles move faster, KE increases, temperature rises.
• - Cooling: Particles move slower, KE decreases, temperature falls.
• - Absolute zero: 0 K or -273.15^°C, minimum kinetic energy.
• - At absolute zero: Pressure is zero, particle motion is minimal.
• - Kelvin scale: Absolute temperature scale starting at absolute zero.

Remember

• - Temperature = Average KE of particles.
• - Heating → faster particles → higher temperature.
• - Cooling → slower particles → lower temperature.
• - Absolute zero = 0 K = -273.15^°C.
• - T ∝ Average KE.
• - Kelvin scale is the absolute scale.

Common Mistakes

• - Thinking temperature is the total kinetic energy: Temperature is the average kinetic energy, not the total. A large container of water at 50°C has more total kinetic energy than a small cup of water at 50°C, but the average kinetic energy of the particles is the same, so the temperature is the same.
• - Thinking particles stop completely at absolute zero: In classical physics, they would stop. In quantum mechanics, they still have some zero-point energy. However, for most practical purposes, we say they have minimum kinetic energy.
• - Confusing temperature with heat: Temperature is a measure of the average kinetic energy of particles. Heat is the transfer of energy from a hotter object to a colder one.

Quick Revision

The temperature of a substance is a measure of the average kinetic energy of its particles. When a substance is heated, its particles move faster, increasing their kinetic energy, and the temperature rises. When cooled, the particles move slower, decreasing their kinetic energy, and the temperature falls. Absolute zero is the lowest possible temperature, at which particles have the minimum possible kinetic energy.

60-Second Revision

• Heating: Faster particles, higher temperature.
• Cooling: Slower particles, lower temperature.
• Absolute zero: 0 K or -273.15^°C.
• T ∝ Average KE.
• Kelvin scale: Absolute scale.

Frequently Asked Questions (FAQs)

Q1. What is the relationship between temperature and particle motion? Answer: Temperature is directly proportional to the average kinetic energy of the particles in a substance. When particles move faster (higher kinetic energy), the temperature is higher. When they move slower (lower kinetic energy), the temperature is lower.

Q2. What happens to the particles when a substance is heated? Answer: When a substance is heated, its particles absorb energy and move faster. This increases their kinetic energy, which raises the temperature of the substance.

Q3. What happens to the particles when a substance is cooled? Answer: When a substance is cooled, its particles lose energy and move slower. This decreases their kinetic energy, which lowers the temperature of the substance.

Q4. What is absolute zero? Answer: Absolute zero is the lowest possible temperature, at which particles have the minimum possible kinetic energy. It is 0 K on the Kelvin scale or -273.15^°C on the Celsius scale.

Q5. Why does the pressure of a gas increase when it is heated? Answer: When a gas is heated, its particles move faster and collide with the container walls more frequently and with greater force. This increases the pressure.

Q6. What is the difference between temperature and heat? Answer: Temperature is a measure of the average kinetic energy of the particles in a substance. Heat is the transfer of energy from a hotter object to a colder one due to a temperature difference.

Q7. Why is the Kelvin scale used in scientific calculations? Answer: The Kelvin scale is an absolute temperature scale that starts at absolute zero. It is used in scientific calculations because it is directly proportional to the average kinetic energy of particles and has no negative values.

Multiple Choice Questions (MCQs)

• Q1. The temperature of a substance is a measure of the average:
• A. Potential energy of particles
• B. Kinetic energy of particles
• C. Mass of particles
• D. Volume of particles

• Correct Answer: B
• Explanation: The text states that the temperature of a substance is directly proportional to the average K.E. of its particles.

• Q2. When a substance is heated, its particles:
• A. Move slower
• B. Move faster
• C. Stop moving
• D. Change color

• Correct Answer: B
• Explanation: The text states that when we heat a substance, the speed and kinetic energy of its particles increase.

• Q3. When a substance is cooled, its particles:
• A. Move faster
• B. Move slower
• C. Stop moving completely
• D. Increase in mass

• Correct Answer: B
• Explanation: The text states that when heat is removed, the speed and kinetic energy of the particles become slower.

• Q4. Absolute zero is the temperature at which:
• A. Particles move at maximum speed
• B. Particles have minimum kinetic energy
• C. Water boils
• D. Ice melts

• Correct Answer: B
• Explanation: The text states that at absolute zero, particles have least or no kinetic energy.

• Q5. Absolute zero is equal to:
• A. 0^°C
• B. 100^°C
• C. 0 K or -273.15^°C
• D. 273 K

• Correct Answer: C
• Explanation: The text states that absolute zero is 0 K on the Kelvin scale and -273.15^°C on the Celsius scale.

• Q6. Temperature is directly proportional to:
• A. The total kinetic energy of particles
• B. The average kinetic energy of particles
• C. The mass of the substance
• D. The volume of the substance

• Correct Answer: B
• Explanation: The text states that temperature is directly proportional to the average K.E. of its particles.

• Q7. The Kelvin scale starts at:
• A. 0^°C
• B. 100^°C
• C. Absolute zero
• D. The boiling point of water

• Correct Answer: C
• Explanation: The Kelvin scale is an absolute temperature scale that starts at absolute zero.

• Q8. Which of the following is true about the relationship between temperature and particle motion?
• A. As temperature increases, particle motion decreases.
• B. As temperature increases, particle motion increases.
• C. Temperature has no effect on particle motion.
• D. Particle motion is independent of temperature.

• Correct Answer: B
• Explanation: The text states that when a substance is heated, the speed and kinetic energy of its particles increase, which increases the temperature.

• Q9. At absolute zero, the pressure of an ideal gas is:
• A. Maximum
• B. Minimum but non-zero
• C. Zero
• D. Infinite

Correct Answer: C Explanation: The text states that at absolute zero, particles cannot collide with each other or with the container, therefore they cannot exert pressure (P=0 Pa).

• Q10. The average kinetic energy of particles in a gas is given by:
• A. kT
• B. 32kT
• C. 2kT
• D. 12kT

• Correct Answer: B
• Explanation: The average kinetic energy of particles in a gas is 32kT, where k is the Boltzmann constant and T is the absolute temperature.

Frequently Asked Questions (FAQs)

Q1. What is the difference between temperature and kinetic energy? Answer: Temperature is a measure of the average kinetic energy of the particles in a substance. Kinetic energy is the energy of motion of individual particles. Temperature is a macroscopic property that reflects the average kinetic energy of the microscopic particles.

Q2. Why does a large object at the same temperature have more total kinetic energy? Answer: A larger object has more particles, so even though the average kinetic energy per particle is the same, the total kinetic energy (sum of all particles' kinetic energy) is greater.

Q3. What is the Boltzmann constant? Answer: The Boltzmann constant (k) relates the average kinetic energy of particles in a gas to the temperature: KE_avg = 32kT. Its value is approximately 1.38 × 10^-23 J/K.

Q4. Why is absolute zero considered the lowest possible temperature? Answer: Because at absolute zero, particles have the minimum possible kinetic energy. According to classical physics, they would have zero kinetic energy. According to quantum mechanics, they still have some zero-point energy, but no heat can be extracted from the system.

Q5. How does the Kelvin scale relate to the Celsius scale? Answer: The Kelvin scale starts at absolute zero (0 K), while the Celsius scale starts at the freezing point of water (0^°C). The relationship is: T(K) = T(^°C) + 273.15 For example, 0^°C = 273.15 K.

Q6. What happens to the particles of a substance at absolute zero? Answer: At absolute zero, particles have the minimum possible kinetic energy. In classical physics, they would stop moving completely. In quantum mechanics, they still have some residual motion (zero-point energy), but they cannot transfer heat to anything else.

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