General Concepts

1. General Concepts • Thermodynamics is the branch of physics concerned with heat and its relation to energy and work. It defines macroscopic variables (such as temperature, internal energy, entropy, volume, and pressure) that characterize macroscopic substances (materials and radiation), and explains how they are related and by what laws they change with time. Thermodynamics describes the average behavior of very large numbers of microscopic constituents, and its laws can be derived from statistical mechanics. • Specifically, thermodynamics focuses largely on how a heat transfer is related to various energy changes within a physical system undergoing a thermodynamic process. Such processes usually result in work being done by the system and are guided by the laws of thermodynamics. • Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854: • Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency. Lord Kelvin is widely known for determining the correct value of absolute zero as approximately -273.15 Celsius. A lower limit to temperature was known prior to Lord Kelvin, as shown in "Reflections on the Motive Power of Heat", Sadi Carnot, ~1820, before Lord Kelvin's birth in 1824. "Reflections" used -267 as the absolute zero temperature. Absolute temperatures are stated in units of kelvin in his honor. William Thomson, 1st Baron Kelvin (1824 – 1907)

2. Cannon boring experiment Rumford's most important scientific work took place in Munich, and centered on the nature of heat, which he contended in An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction (1798) was not the caloric of then-current scientific thinking but a form of motion. Rumford had observed the frictional heat generated by boring cannon at the arsenal in Munich. Rumford immersed a cannon barrel in water and arranged for a specially blunted boring tool. He showed that the water could be boiled within roughly two and a half hours and that the supply of frictional heat was seemingly inexhaustible. Rumford confirmed that no physical change had taken place in the material of the cannon by comparing the specific heats of the material machined away and that remaining. Sir Benjamin Thompson, Count Rumford (1753 –1814) Rumford stated, in reaction to this un-explained phenomenon of the production of heat without fire, that “it would be difficult to describe the surprise and astonishment expressed in the countenances of the bystanders, on seeing so large a quantity of cold water heated, and actually made to boil, without any fire.”

3. Ice rubbing experiment This experiment was conducted in 1799 by English chemical physicist Humphry Davy, in which he rubbed two pieces of ice, located inside of a room colder than the freezing point of water, together, vigorously, to see if he could generate heat by friction, an idea contrary to the then-prevalent “caloric theory” of French chemist Antoine Lavoisier, which supposed that the ice would only melt if put in contact with a hotter body, thereby releasing the flow of caloric particles into the ice, causing it to melt. The significance of Davy’s ice-rubbing experiment helped to prove that heat was a mode of motion. The mechanical equivalent of heat thermometer paddle water Joule's apparatus for measuring the mechanical equivalent of heat The small calorie or gram calorie (symbol: cal) approximates the energy needed to increase the temperature of 1 gram of water by 1 °C at standard atmospheric pressure (101.325 kPa). This is approximately 4.184 joules (1 J = N⋅m). James Prescott Joule (1818 – 1889) English physicist and brewer Joule wrote in his 1845 paper: ... the mechanical power exerted in turning a magneto-electric machine is converted into the heat evolved by the passage of the currents of induction through its coils; and, on the other hand, that the motive power of the electro-magnetic engine is obtained at the expense of the heat due to the chemical reactions of the battery by which it is worked.

4. The thermodynamicists representative of the original eight founding schools of thermodynamics. The schools with the most-lasting effect in founding the modern versions of thermodynamics are the Berlin school, particularly as established in Rudolf Clausius’s 1865 textbook The Mechanical Theory of Heat, the Vienna school, with the statistical mechanics of Ludwig Boltzmann, and the Gibbsian school at Yale University, American engineer Willard Gibbs' 1876 On the Equilibrium of Heterogeneous Substances launching chemical thermodynamics. Statistical mechanics or statistical thermodynamics is a branch of physics that applies probability theory, which contains mathematical tools for dealing with large populations, to the study of the thermodynamic behavior of systems composed of a large number of particles. Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in everyday life, thereby explaining thermodynamics as a result of the classical and quantum-mechanical descriptions of statistics and mechanics at the microscopic level.

5. Temperature Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot. When a heat transfer path between them is open, heat spontaneously flows from bodies of a higher temperature to bodies of lower temperature. The flow rate increases with the temperature difference, while no heat will be exchanged between bodies of the same temperature, which are then said to be in "thermal equilibrium". For monoatomic gases acting like point masses, a higher temperature simply implies higher average kinetic energy. Faster molecules striking slower ones at the boundary in elastic collisions will increase the velocity of the slower ones and decrease the velocity of the faster ones, transferring energy from the higher temperature to the lower temperature region. With time, the molecules in the two regions approach the same average kinetic energy (same temperature) and in this condition of thermal equilibrium there is no longer any net transfer of energy from one object to the other. The concept of temperature is complicated by internal degrees of freedom like molecular rotation and vibration and by the existence of internal interactions in solid materials which can include collective modes. The internal motions of molecules affect the specific heats of gases, with diatomic hydrogen being the classic case. Collective modes affect the specific heats of solids, particularly at low temperatures.

6. "Temperature is a measure of the tendency of an object to spontaneously give up energy to its surroundings. When two objects are in thermal contact, the one that tends to spontaneously lose energy is at the higher temperature.” (Thermal Physics, Ch. 1) Zeroth law of thermodynamics The zeroth law states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. Systems are said to be in thermal equilibrium if they are able to transfer heat between each other (for example by conduction or radiation) but do not do so. The law implies that thermal equilibrium between systems is a transitive relation, which affords the definition of an empirical physical parameter, called temperature. The temperatures are equal for all systems in thermal equilibrium. The law permits the construction of a thermometer to measure this property Absolute zero Absolute zero is the theoretical lowest possible temperature. More formally, it is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means. A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state. The kinetic energy of the ground state cannot be removed. However, in the classical interpretation, it is zero and the thermal energy of matter vanishes. The zero point of any thermodynamic temperature scale, such as Kelvin scale, is set at absolute zero. By international agreement, absolute zero is defined as 0K on the Kelvin scale and as −273.15° on the Celsius scale. This equates to −459.67° on the Fahrenheit scale. Scientists have achieved temperatures very close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity.

8. Cosmic microwave background radiation Cosmic microwave background radiation (or relic radiation) is thermal radiation filling the observable universe almost uniformly. With a traditional optical telescope, the space between stars and galaxies (the background) is completely dark. However, a sufficiently sensitive radio telescope shows a faint background glow, almost exactly the same in all directions, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The CMB's serendipitous discovery in 1964 by American radio astronomers Arno Penzias and Robert Wilson earned them the 1978 Nobel Prize. Cosmic background radiation is well explained as radiation left over from an early stage in the development of the universe, and its discovery is considered a landmark test of the Big Bang model of the universe. Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. The CMBR has a thermal black body spectrum at a temperature of 2.725 K, which peaks at the microwave range frequency of 160.2 GHz, corresponding to a 1.873 mm wavelength.

9. The ideal gas An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. At normal conditions such as standard temperature and pressure, most real gases behave qualitatively like an ideal gas. Many gases such as air, nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated like ideal gases within reasonable tolerances. Generally, a gas behaves more like an ideal gas at higher temperature and lower density (i.e. lower pressure), as the work performed by intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. The equation of state of a classical ideal gas is the ideal gas law: P =pressure, V=volume, n=number of moles, R=universal gas constant (8.314 J·K−1mol-1), T=temperature (in kelvins). A mole of molecules is Avogadro’s number of them: number of molecules Boltzmann’s constant

10. Boyle’s law Boyle's law states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, if the temperature remains unchanged within a closed system. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662.

11. Microscopic Model of Ideal Gas • Assumptions • At any moment, the velocity of the molecule is v=(vx, vy, vz) • Collisions with the wall are always elastic (|v| is always constant) • Perfectly smooth surfaces: the molecule’s path as it bounces is symmetrical about a line normal to the surface, just like bouncing light from a mirror During the time the molecule undergoes exactly one collision with the piston, and the change in vx is This gives: For N molecules:

12. The average kinetic energy is: The temperature of a gas is proportional to the average translational kinetic energy of its molecules! At room temperature: kT = (1.38 x 10-23 J/K) (300 K) = 4.14 x 10-21 J An electron-volt (eV) is the kinetic energy of an accelerated electron through a voltage difference of 1 volt. In eV, kT = 0.026 eV= 1/40 eV, i.e., molecular energies at room temperature are rather small. But… small molecules at ordinary temperatures are bouncing around at hundreds of m/s.