TJC 13 Thermodynamic Systems

Temasek Junior College 1 13 Thermodynamic Systems Learning Outcomes Students should be able to: (a) show an understanding that the macroscopic state of a system determines the internal energy of the system, and that internal energy can be expressed as the sum of a random distribution of microscopic kinetic and potential energies associated with the particles of the system. (b) show an understanding that the thermodynamic temperature of a system is (directly) proportional to the mean microscopic kinetic energy of particles. (c) show an understanding that when two systems are placed in thermal contact, energy is transferred (by heating) from the system at higher temperature to the system at lower temperature, until they reach the same temperature and achieve thermal equilibrium (i.e. no net energy transfer). (d) show an understanding of the difference between the work done by a gas and the work done on a gas, and calculate the work done by a gas in expanding against a constant external pressure: 𝑊 = 𝑝∆𝑉. (e) recall and apply the zeroth law of thermodynamics that if two systems are both in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. (f) recall and apply the first law of thermodynamics, ∆𝑈 = 𝑄 + 𝑊, that the increase in internal energy of a system is equal to the sum of the energy transferred to the system by heating and the work done on the system. (g) define and use the concepts of specific heat capacity and specific latent heat. student copy

Temasek Junior College 2 1 Internal Energy LO (a), (b) We have seen from the previous topic that molecules of a gas possess kinetic energies due to their random motion. Not all molecules have the same kinetic energy because they are moving with different speeds, but the sum of all the kinetic energies will be a constant at that particular temperature. For a real gas, because the molecules exert intermolecular forces on each other, there will be a certain potential energy due to the forces between the molecules and their positions relative to each other. Thus for a real gas, the internal energy is given by the sum of the potential energies and the kinetic energies of all the molecules. The internal energy U, of a system, is the sum of a random distribution of kinetic and potential energies associated with the molecules of a system.  += cmicroscopicmicroscopi EPEKU .... Microscopic kinetic energy • The microscopic KE arises from the continuous random motion of the particles. • For monatomic gases, the microscopic KE refers to translational motion of atoms. • For diatomic and polyatomic gases, the kinetic energies include other forms such as rotational and vibrational kinetic energies of the molecules. The temperature T of a gas is a measure of the mean kinetic energy of particles in the gas. Fig. 3 The molecules of a gas have both kinetic and potential energies.

Temasek Junior College 3 Microscopic potential energy • The microscopic PE arises from the intermolecular forces and they depend on the type of bond between the particles and the intermolecular separation. • Potential energy is the highest when the particles are separated far apart, and the potential energy drops as the particles are nearer. This is similar to gravitational potential energy: the potential energy is high when the object is high above the ground and low when the object is subjected to the gravitational attractive force and moves nearer to the ground. Ideal Gas For an ideal gas, there are no intermolecular forces. Therefore, the potential energy of the molecules is zero. The internal energy of an ideal gas is simply equal to the total kinetic energy of the molecules. Note: • U is proportional to the product NT or nT or pV. • For a fixed amount of an ideal gas, U  T. When temperature changes by T, the change in internal energy, TnRU = 2 3 . Evaporation Evaporation is the process by which a liquid becomes vapour at any temperature. For a given external pressure, the evaporation rate increases with temperature, reaching a maximum at boiling point. Due to the continual motion and collisions between the molecules in a liquid, their speeds change continually. Consider a molecule reaching the surface from within the liquid. If it has a kinetic energy large enough to do work against the attractive forces of the other molecules in the liquid and against the atmospheric pressure, then it is able to escape from the liquid to become a molecule of a vapour. During evaporation, since molecules having larger kinetic energies escape, the average kinetic energy of the remaining molecules in the liquid decreases. Therefore the temperature drops and the liquid cools. possible for molecule to escape if it has sufficient kinetic energy air molecule attractive force due to other molecules liquid internal energy of an ideal gas U = 2 3 NkT = 2 3 nRT = 2 3 pV

Temasek Junior College 4 2 Temperature 2.1 Temperature and Heat From the macroscopic perspective between systems, temperature is the physical property that determines the direction of heat flow. Heat then refers to the energy transferred between two systems at different temperatures. Microscopically however, we can define temperature as a measure of the average kinetic energy of molecules in a body. 2.2 Thermal Equilibrium LO(c), (e) When two bodies of different temperatures are in thermal contact, net heat energy is transferred from the body at higher temperature to that at lower temperature. This heat transfer bring s about a change in the microscopic kinetic and potential energies of the two bodies. For instance, to measure the temperature of a cup of hot coffee, a thermometer is placed into the coffee. As the two bodies (hot coffee and thermometer) interact, the thermometer becomes hotter and the coffee cools off a little. After the thermometer settl es down to a steady value, you read the temperature. The system of coffee and thermometer has reached an equilibrium, in which the interaction between the thermometer and the coffee causes no further change in the system. We call this a state of thermal equilibrium. Two bodies in thermal contact are said to be in thermal equilibrium when there is no net flow of heat from one body to another. It also implies that the two bodies are at the same temperature. Consider the two systems above, X and Y: Fig 1: no thermal contact  no flow of heat between X and Y. Fig 2: X and Y in thermal contact. Since temperature of X  temperature of Y,  net heat flows from X to Y,  temperature of X decreases while that of Y increases. Fig 3: X and Y in thermal equilibrium.  no net flow of heat between X and Y,  temperature of X = temperature of Y X Y YX Y X Fig. 1 Fig. 2 Fig. 3 insulator

Temasek Junior College 5 Note: Heat cannot be stored. Heat refers to the energy transferred between two bodies at different temperatures. Example 1 A solid X is in thermal equilibrium with a solid Y, which is at the same temperature as a third solid Z. The three bodies are of different materials and masses. Which one of the following statements is certainly true? A It is not necessary that Y should be in thermal equilibrium with Z. B It is not necessary that X should be at the same temperature as Z. C There is no net transfer of energy if X is placed in thermal contact with Z This shows the zeroth law of thermodynamics: if two systems are both in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.

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