Thermal Physics B lecture notes

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-1 H2 Topic 6B Thermal Physics (II)

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-2 Content  Kinetic Theory of Matter  Internal Energy  Ideal Gases and the Ideal Gas Law  Internal Energy of an Ideal Gas  The First Law of Thermodynamics  P-V Diagrams Learning Outcomes Candidates should be able to (a) show an understanding that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system. (b) relate a rise in temperature of a body to an increase in its internal energy. (c) explain using a simple kinetic model for matter why i. melting and boiling take place without a change in temperature, ii. the specific latent heat of vaporisation is higher than specific latent heat of fusion for the same substance, iii. cooling effect accompanies evaporation. (d) recall and use the first law of thermodynamics expressed in terms of the change in internal energy, the heating of the system and the work done on the system. (e) recall and use the ideal gas equation pV = nRT, where n is the amount of gas in moles. (f) show an understanding of the significance of the Avogadro constant as the number of atoms in 0.012 kg of carbon-12.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-3 (g) use molar quantities where one mole of any substance is the amount containing a number of particles equal to the Avogadro constant. (h) recall and apply the relationship that the mean kinetic energy of a molecule of an ideal gas is proportional to the thermodynamic temperature to new situations or to solve related problems.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-4 INTRODUCTION Now that we have dealt with how we perceive heat and thermal energy at a macroscopic level, let us deal with how heat manifests at a microscopic level. In this set of lecture n otes, we’ll be dealing with the kinetic theory of matter, and thermodynamics. 6.3 KINETIC THEORY 6.3.1 The Kinetic Model of Matter Learning Outcome (a) show an understanding that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system. The kinetic model of matter refers to the theory that attempts to explain the macroscopic behaviour of matter in terms of their microscopic properties. Key to this model is the simple assumption that all matter is made of atoms/molecules. Any atom in a substance possesses two different kinds of energies, that being kinetic, and potential energy. Random kinetic energy refers to the energy associated with how fast the particle is moving in the frame of the object . The average random kinetic energy of all atoms in a substance is associated with an object’s temperature. If a substance has experienced an increase in temperature, we know that on average, the particles are moving faster. Note: The random kinetic energy of the particle m ust be contrasted with the bulk translational kinetic energy. The bulk translational kinetic energy refers to the energy that is associated to motion of the entire object in the lab reference frame.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-5 Potential energy refers to the energy associated with t he intermolecular forces of attraction. The potential ene rgy is associated with the phase of a substance, and how far apart the atoms are in the substance. If a substance has increased its potential energy, we know that the intermolecular spacing between p articles has increased, and/or a ch ange of phase (from solid to liquid or from liquid to gas) has taken place. Note: The value of potential energy is a negative value. This is because energy has to be supplied to the atoms in order to free them from the influence of the other atoms. If for example, the potential energy of a particular atom is -5 J, this means that 5 J has to be supplied in order to free it from the force of attraction due to the other atoms. A potential energy of 0 J implies that the atom is completely free. The internal energy of a substance is the sum of kinetic energy due to the random motion of all particles, and the potential energy due to the intermolecular forces of attraction. U = KEtotal + PEtotal

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-6 Learning outcome (c) explain using a simple kinetic model for matter why i. melting and boiling take place without a change in temperature. Solution: When melting and boiling takes place,  energy is being used to break the intermolecular bonds and the increase the potential energy of the substance.  As the average kinetic energy of the system does not increase, the temperature remains the same. ii. the specific latent heat of vaporisation is higher than specific latent heat of fusion for the same substance, Solution: When a substance is changing from solid to liquid,  the intermolecular bonds are being partially broken and  the intermolecular spacing does not increase much. When a substance is changing from liquid to gas,  the intermolecular bonds are being broken further and  the intermolecular spacing between molecules increases significantly.  Furthermore, work has to be done to overcome atmospheric pressure. As such, the specific latent heat vaporisation is larger than the specific latent heat of fusion.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-7 iii. Cooling effect accompanies evaporation. Solution The molecules of a liquid have varying kinetic energies.  The most energetic molecules at the surface obtain energy from the environment (through collision with air particles, or radiant sunlight)  These molecules thus obtain enough energy to break free of the intermolecular bonds of attraction and leave the system.  As the most energetic molecules are leavi ng the system, the average kinetic energy of the system decreases.  This causes the temperature of the system to fall.  Heat is drawn from the external environment and cooling effect accompanies.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-8 6.3.2 Kinetic Theory of Gases The kinetic theory of gases makes several assumptions. (a) A gas consists of particles called atoms/molecules. (b) The total number of molecules is very large. (c) The molecules are in constant, random motion and obey Newton’s laws of motion. (d) The pressure on the container is the result of collisions with the walls as the molecules strike and rebound. For gases, four macroscopic variables are of utmost importance. They are, namely, 1. Amount of gas (number of molecules/moles) 2. Volume 3. Pressure 4. Temperature We shall collectively refer to these four as the “state variables” of the gas. From now on, whenever we talk about the “state” of a gas, we are really talking about thes e four quantities. With knowledge of the state variables, we are also able to determine the inter nal energy of the system. You would do well to remember the following statement. The internal energy of a substance is a function of its state.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 6B: Thermal Physics (II) 6B-9 6.3.3 Gas Laws and The Equation of State Learning outcomes: (e) recall and use the ideal gas equation pV = nRT, where