RI Chap 13 Thermodynamic Systems Lecture Notes

13 THERMODYNAMIC SYSTEMS H2 Physics 9478 Content Page 13.1 Internal energy 3 13.2 Heating and work done 9 13.3 Laws of thermodynamics 10 13.4 Specific heat capacity and specific latent heat 25 13.5 Appendix 39 Learning Outcomes Candidates 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 pV= ∆ . (e) recall and use 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, UQW∆=+ , that the increase in internal energy of a system is equal to the sum of the heat supplied to the system and the work done on the system. (g) define and use the concepts of specific heat capacity and specific latent heat.

Page | 2 Thermodynamic Systems – An Overview The first law of thermodynamics is central to understanding thermodynamic processes which involve heat transfer and mechanical work. This law is an extension of the conservation of energy used in mechanics as it considers energy exchange in a system by means of both heat transfer and mechanical work. Through the ways which energy can be transferred between a system and its surroundings, changes in the internal energy of the system can result. The concept of internal energy is introduced to make the link between heat and mechanical work to measurable macroscopic properties like pressure, volume and temperature. This internal energy is also related to microscopic kinetic and potential energies associated with the particles of the system. Linking the ideas about heat and temperature is the zeroth law of thermodynamics, which states that when two objects at different temperature are placed in thermal contact, there will be energy exchange between them until thermal equilibrium is reached. The zeroth law allows the use of thermometers to measure temperature. When thermal equilibrium is achieved, the thermometer reflects its own temperature which is of the same value as the other body that it is in thermal contact with. Energy transfer between two substances in thermal contact usually results in temperature changes in both, though this is not so during a change of phase. Heat capacity and specific heat capacity allow for the calculation of temperature changes in such interactions. Similarly, latent heat is used to calculate the energy required to change the phase of a substance (e.g. from solid to liquid, or from liquid to gas).

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT 3 | Page 13.1 Internal Energy  Properties of molecules in different phases Matter is made up of a large number of molecules, which are particles whose dimensions are about 1010− m. Evidence for the existence of molecules is given by experiments demonstrating Brownian motion (refer to Appendix in Chapter 12). There are three phases of matter: solid, liquid and gas. Table 13.1 is a summary of their characteristics and shows the difference between the phases. Solid Liquid Gas Packing arrangement of atoms/ molecules Atoms / molecules are closely packed in a regular pattern called a lattice structure (regular, geometrical structure) Atoms / molecules are slightly further apart than in solids Atoms / molecules are significantly further apart Illustration Crystal Lattice Structure Liquid atoms / molecules Gas atoms / molecules Interatomic distance 103 10 m−≈× 103 10 m−≈× −9~ 10 m Density High High Low Volume/ shape fixed volume and shape fixed volume but takes the shape of the container no fixed volume or shape and fills up entire space / container in which they are placed in Compression return to their original shape when stretched or compressed (to a certain extent) almost incompressible easily compressed Movement of atoms/ molecules limited to vibrations of the atoms / molecules about their mean positions random motion throughout the liquid random motion at high speeds throughout the space occupied Inter-atomic/ molecular forces strong intermolecular attractive and repulsive forces attractive cohesive forces (pulls back the molecules near the surface of the liquid, opposing their escape) no long-range order negligible attractive/repulsive forces between atoms / molecules (because they are very far apart) Table 13.1

Page | 4  Microscopic kinetic energy The microscopic kinetic energy (KE) of a body is due to the kinetic energies of its particles due to their constant random motion, which can be translational, rotational or vibrational as shown in Fig. 13.1. Fig. 13.1 In a body , there is a large number of particles in it ( one mole contains 6.02 × 1023 particles), and each particle has its own individual microscopic KE. It is usually not meaningful to consider individual particle’s microscopic KE, hence we consider their average microscopic KE instead. The temperature of a body is dependent on the average microscopic KE of all its particles (for ideal gas, temperature is directly proportional to the average microscopic KE). In other words, the faster the movement of a body’s particles, the higher its temperature. In fact, the Kelvin scale was designed such that 0 K is the temperature at which the average microscopic KE is zero and all particles are stationary – but this is physically impossible to achieve. Heating a body transfers heat to the body. If it increases the microscopic KE of the body’s particles, then the average microscopic KE of the body increases and hence its temperature increases.  Microscopic potential energy The microscopic potential energy (PE) of a body is due to the potential energies of its particles, arising from the interactions between them. The microscopic PE of an ideal gas is defined to be zero, and since heat is required for a liquid to change into the gaseous phase, we can deduce that the microscopic PE of liquids must be lower than for gases and that microscopic PE of liquids is negative. Similarly, since heat is required for a solid to change into the liquid phase, the microscopic PE of solids is also negative and lower than that of liquids. When a solid changes into the liquid phase, its microscopic PE is increased as the bonds are being broken. Similarly, when a liquid changes into the gaseous phase, its microscopic PE is increased as the bonds are being broken.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT 5 | Page  Internal energy of a system The state of a system can be described by its state variables, namely its pressure, volume, number of moles, and temperature. The internal energy of the system is determined by the state of this system. We can relate the internal energy (macroscopic property) to the KE and PE of the molecules (microscopic properties) in a body or system. The KE and PE of the molecules that make up the internal energy do not include those due to the bulk movement or position of the whole body or system. For