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Lecture 1: Preliminaries. Schroeder Ch. 1 Gould and Tobochnik Ch. 2.1 – 2.7. What is Thermal Physics?. Thermal physics = Thermodynamics + statistical mechanics Thermodynamics provides a framework of relating the macroscopic properties of a system to one another.
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Lecture 1: Preliminaries Schroeder Ch. 1 Gould and Tobochnik Ch. 2.1 – 2.7
What is Thermal Physics? • Thermal physics = Thermodynamics + statistical mechanics • Thermodynamics provides a framework of relating the macroscopicproperties of a system to one another. • It is concerned only with macroscopic quantities and ignores the microscopic variables that characterize individual molecules • Statistical Mechanics is the bridge between the microscopic and macroscopic worlds: it links the laws of thermodynamics to the statistical behavior of molecules.
Thermodynamic Systems • A thermodynamic system is a precisely specified macroscopic region of the universe together with the physical surroundings of that region, which determine processes that are allowed to affect the interior of the region. • A thermodynamic system can be classified in three ways: • Open systems can exchange both matter and energy with the environment. • Closed systems can exchange energy but not matter with the environment. • Isolated systems can exchange neither energy nor matter with the environment.
Thermodynamic State • A thermodynamic state is the macroscopic condition of a thermodynamic system as described by a suitable set of parameters known as state variables. • Examples of state variables are temperature, pressure, density, volume, composition, and entropy. • Thermodynamic variables are often divided into two categories: • Intensive variables • Extensive variables
Pressure and Mechanical Equilibrium • Let be an surface element of the surface of this piston where the direction is the outward normal. • Let be the force normal to the surface element. • We can define the pressure as • If the pressure is constant, then the pressure of the gas exerted on the piston is • We say that two systems in contact with one another are in mechanical equilibrium when their pressures are equal.
Temperature and Thermal Equilibrium • Consider two thermodynamic systems, A and B, that are brought into contact with one another. • Over a period of time, the net exchange of energy between both systems ceases and we say that they are in thermal equilibrium. • Thermal equilibrium is determined by a single variable called the temperature.
The Zeroth Law of Thermodynamics • Thermal equilibrium satisfies the zeroth law of thermodynamics which states • If two thermodynamic systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. • The zeroth law of thermodynamics ensures that thermal equilibrium is determined solely by temperature.
Thermometers • We can use thermometric properties to build thermometers by defining the scale of temperature in such a way that for any thermometric property X, • We can define the two constants, and , that define this linear scale by choosing two reproducible phenomenon that always occur at the same temperature. • We choose • The boiling point of pure water at sea level • Triple point of pure water
Temperature Scales • Using these properties, we have that • Choosing and gives the Celsius scale • Choosing and gives the Fahrenheit scale
Constant Volume Gas Thermometer • The gas flask is inserted into an ice–water bath, and mercury reservoir B is raised or lowered until the volume of the confined gas is at some value, indicated by the zero point on the scale. • The height h, the difference between the levels in the reservoir and column A, indicates the pressure in the flask at 0°C. • The flask is inserted into water at the steam point, and reservoir B is readjusted until the height in column A is again brought to zero on the scale, indicating the pressure in the flask at 100°C.
Constant Volume Gas Thermometer • The line connecting two points on the pressure vs. temperature curve serves as a calibration curve for measuring unknown temperatures. • The height of the mercury column tells us the pressure of the gas, and we could then find the temperature of the substance from the calibration curve.
The Kelvin Scale • If we now plot the pressure vs. temperature as measured by our thermometer for different gases, we obtain a linear curve. • Notice that the pressure is exactly zero at for all cases. • This is often called absolute zero and serves as the basis for a new temperature scale called the Kelvin scale.
Ideal Gas Law • An equation of state is an equation that relates macroscopic variables for a given substance in thermodynamic equilibrium. • The most famous equation of state is the ideal gas law • Here is the number of moles present in the gas and R is the ideal gas constant • The ideal gas law can also be written in terms of the molecules present in the gas • Here, is the number of molecules in the gas and k is the Boltzmann’s constant.
The Kinetic Theory of Gases • In the previous section, we discussed the macroscopic properties of an ideal gas. • Now, we consider the ideal gas model from a microscopic point of view using kinetic theory. • The kinetic theory of gases makes the following assumptions • All molecules in the gas are identical • The molecules interact only through short-range forces during elastic collisions • The molecules obey Newton’s laws of motion • The number of molecules in the gas is large • The average separation between molecules is larger compared with their dimensions
The Kinetic Theory of Gases • Consider a one-dimensional gas in a one-dimensional box of length L. • The change in momentum after the molecule collides with the wall is • Since the molecule must travel a distance 2L before returning to the same wall, the rate at which the molecules imparts momentum to the wall is
The Kinetic Theory of Gases • If there are N molecules in the box, then the force on the wall is • The pressure on the wall is given by • Since the molecules are equally probable to move in all three directions of space, then we have
The Kinetic Theory of Gases • Comparing our previous result with the ideal gas law, we see that temperature is associated with the mean kinetic energy of the molecules • We can also obtain a relationship between the pressure of a gas, its density, and the root mean square speed .
Thermodynamic Processes • A thermodynamic process is any process that takes a macroscopic system from one equilibrium state to another. • We will be concerned with energy conservation in thermodynamic processes and thus it will be important to define two important variables • Work • Heat
Definition of Work • Let be an surface element of the surface of this piston where the direction is the outward normal. • Let be the net force exerted by the system on the surface element of the boundary. • Suppose that the boundary experiences a deformation so that the surface element is displaced by . • The work done by the system on the boundary is
Quasistatic Processes • Quasi-static (quasi-equilibrium) processes –sufficiently slow processes, any intermediate state can be considered as an equilibrium state • For quasistatic processes, the state variables (e.g. pressure, volume, temperature) are well defined. • Examples of quasi-equilibrium processes: • Isochoric (constant volume) • Isobaric (constant pressure) • Isothermal (constant temperature)
Thermodynamic Diagrams • The evolution of a thermodynamic system can be given by a thermodynamic diagram. • Because there is one equation of state, all processes will occur in a two-dimensional plane, which can be spanned by any of the three possible pairs: (p,V), (p,T), and (V,T). • The area under the graph in a PV diagram is equal in magnitude to the work done on the gas.
Work in Thermodynamic Processes • For an isochoric process, no work is done since . • For an isothermal process, the work done is • For an isobaric process, the work done is
Heat • Heatis energy transferred into or removed from a macroscopic system on the molecular level, as opposed to the direct application of mechanical work on the system by deformations of its macroscopic parameters. • The unit of heat is the calorie and it is defined as the energy necessary to raise the temperature of 1 g of water from 14.5⁰C to 15.5⁰C. • Note that 1 calorie is equal to 4.186 J.
Heat Capacity and Specific Heat • We define the heat capacity of a thermodynamic system as the amount of heat required to raise the temperature of the system by one degree Kelvin • Here, is the heat absorbed and is the change of temperature. • We define the specific heat as • In terms of specific heat,
Latent Heat • Energy may be absorbed or released from a system during isothermal processes through phase transitions. • We define latent heat as the heat required to change the phase of one gram of a substance
Calorimetry • Heat capacities, specific heats and latent heats of substances are measured using calorimetry. • Acalorimetric experiment involves the transfer of energy between two or more thermodynamic systems while the combination of the systems is kept isolated from the rest of the universe. • Devices in which the exchange of energy occurs are called calorimeters, whose main function is to isolate whatever is placed inside. • Since the combination of thermodynamic systems is kept isolated, the calorimetric process satisfies
Mechanisms of Heat Transfer • Heat transfer occurs primarily through three processes: conduction, convection, and radiation. • Conduction: the energy transfer by molecular contact • Convection: the energy transfer by macroscopic motion of fluids • Radiation: energy transfer by emission/absorption of electromagnetic radiation.
Conduction • Energy transfer between two macroscopic systems due to a difference in temperature between them and which does not involve the gross movement of matter is called conduction. • Conduction can be understood on the microscopic scale as the direct exchange of mechanical energy from a region of higher temperature to a region of lower temperature by molecular collisions.
Newton’s Law of Heat Conduction • Consider a solid material with a cross-sectional area S of constant temperature within it. • Newton’s law of heat conduction says that, assuming there is a temperature gradient across S, the rate at which energy is transferred across S is given by