Thermal Physics (Thermodynamics)

1. Thermal Physics (Thermodynamics) • Concerned with the concepts of thermal (or internal) energy transfers between a system and its environment and the resulting temperature variations • Temperature is central concept of thermodynamics • Be careful not to trust your (subjective) senses to measure temperature! • Historically, the development of thermodynamics paralleled the development of atomic theory • Concerns itself with the physical and chemical transformations of matter in all of its forms: solid, liquid, and gas • Temperature, heat flow, and internal energies will be studied

2. Zeroth Law of Thermodynamics • The flow of energy that occurs between 2 objects or systems due to a temperature difference between them is called heat flow • Objects are in thermal contact if heat flow can take place between them • Thermal equilibrium exists when two objects in thermal contact with each other cease to exchange energy • Definition of temperature relies on the zeroth law of thermodynamics: If objects A and B are in thermal equilibrium with a third object, C, then A and B are in thermal contact with each other

3. Zeroth Law of Thermodynamics • Less formal definition: Every body has a property called temperature. When 2 bodies are in thermal equilibrium, their temperatures are equal, and vice versa • Zeroth law used constantly in the lab • If we want to know if 2 liquids have same temperature, we measure temperature of each with a thermometer • No need to bring them into thermal contact • Zeroth law came to light only in 1930s, long after 1st and 2nd laws of thermodynamics were established

4. Thermometers • Thermometers are devices used to measure the temperature of an object or a system • Example is mercury thermometer • Make use of physical properties that change with temperature • Many physical properties can be used • volume of a liquid • length of a solid • pressure of a gas held at constant volume • volume of a gas held at constant pressure • electric resistance of a conductor • color of a very hot object

5. Temperature Scales • Thermometers can be calibrated by placing them in thermal contact with an environment that remains at constant temperature • Environment could be mixture of ice and water in thermal equilibrium • Also commonly used is water and steam in thermal equilibrium • An ear thermometer measures infrared radiation from the eardrum – why is this useful? • Celsius scale: Temp. of ice–water (water–steam) mixture defined as 0°C (100°C) • Freezing point vs. boiling point of water • Distance between these 2 points divided into 100 equal segments

6. Temperature Scales • Fahrenheit scale: Most common scale used in the U.S. • Employs a smaller degree than Celsius scale • Uses a different zero of temperature than Celsius scale • Temperature of the freezing point of water is set at 32°F • Temperature of the boiling point of water is set at 212°F • 180 divisions between these 2 points • Conversion between Celsius (TC) and Fahrenheit (TF) temperatures:

7. Gas Thermometer • Ideally, the readings of a thermometer should not depend on material used • Gas thermometer comes close to this ideal • Principle is that pressure of a gas at constant volume increases with temperature • Gas placed in constant-volume container and pressure is measured (manometer in figure above) • Calibrated by measuring pressure at 2 temperatures • Temperature readings are nearly independent of the gas • Pressure varies with temperature when maintaining a constant volume

8. Gas Thermometer • If temperature measurements are performed with gas in flask at different starting pressures at 0°C, the data looks like the graph at right: • In each case, regardless of the gas used, the curves extrapolate to the same temperature (absolute zero)at zero pressure • Gases liquefy and solidify at very low temperatures, so we can’t actually observe this zero-pressure condition • The absolute-zero reference point forms basis of Kelvin temperature scale

9. Kelvin Temperature Scale • Named for British physicist Lord Kelvin (1824–1907) • Units same as those on Celsius scale, but zero point is shifted so that 0 K = –273.15°C: • Modern definition (since 1954) of Kelvin scale defined in terms of two points • First point is absolute zero • Second point is the triple point of water • Triple point is the single point where water can exist as solid, liquid, and gas • Single temperature and pressure • Occurs at 0.01°C and P = 4.58 mm Hg • 1 K = 1/273.16 of temperature of triple point of water

10. Some Kelvin Temperatures and Temperature Scale Comparisons

11. Thermal Expansion • The thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or molecules • At ordinary temperatures, molecules vibrate with a small amplitude • As temperature increases, the amplitude increases • This causes the overall object as a whole to expand • For relatively small changes in temperature, the linear dimensions of object change according to: • Coefficient of linear expansion, a, depends on the material (see Table 10.1) • These are average coefficients (they can vary with temperature)

12. Thermal Expansion • Since the linear dimensions of an object change with temperature, there is also a change in surface area: • And a change in volume: • g = 2a and b = 3a only if a is the same in all directions • Many applications of thermal expansion • Pyrex glass • Expansion joints in bridges and buildings • Rising sea levels due to ocean warming (g= 2a= coefficient of area expansion) (b=3a = coefficient of volume expansion for solids; for fluids, see Table 10.1)

13. Thermal Expansion • Thermostats • Bimetallic strips in thermostats (2 metals expand differently) (abrass> asteel)

14. CQ1: The Statue of Liberty is 93 m tall on a summer morning when the temperature is 20°C. If the temperature of the statue rises from 20°C to 30°C, what is the order of magnitude of the statue’s increase in height? Choose the best estimate, treating the statue as though it were solid copper (a = 17 × 10–6°C–1). • 0.1 mm • 1 mm • 1 cm • 10 cm • 1 m

15. Example Problem #10.23 The band in the figure at right is stainless steel (coefficient of linear expansion a = 17.3  10–6°C–1 ; Young’s modulus Y = 18  1010 N/m2). It is essentially circular with an initial mean radius of 5.0 mm, a height of 4.0 mm, and a thickness of 0.50 mm. If the band just fits snugly over the tooth when heated to a temperature of 80°C, what is the tension in the band when it cools to a temperature of 37°C? Solution (details given in class): 2.7  102 N

16. Thermal Expansion of Water • As the temperature of water decreases from 4ºC to 0ºC, it expands and its density decreases • Above 4ºC, water expands with increasing temperature, typical of other liquids and materials • Maximum density of water is 1000 kg/m3 at 4ºC • This unusual behavior explains why: • ice humps up in the middle of the compartments in an ice cube tray • a lake freezes slowly from the top down (important for animal and plant life!) • water pipes can burst in the winter

17. Ideal Gas • A gas does not have a fixed volume or pressure • In a container, the gas expands to fill the container • Most gases at room temperature and pressure behave approximately as an ideal gas (one in which there is simple relationship between P, V, and T) • Characteristics of ideal gas: • Collection of atoms or molecules that move randomly • Exert no long-range force on one another • Occupy a negligible fraction of the volume of their container • Understanding ideal gases is useful because all real gases approach an ideal gas at low enough densities (when molecules are far enough apart that they do not interact with each other)

18. Ideal Gas • It’s convenient to express the amount of gas in a given volume in terms of the number of moles, n: • One mole is the amount of the substance that contains as many atoms as there are atoms in 12 g of the carbon–12 isotope • 1 mol of a substance contains the same number of atoms as in 1 mol of any other substance • The number of atoms in one mole is called Avogadro’s Number= NA = 6.02 1023 atoms/mol • We can use this number to calculate the mass of an individual atom:

19. Ideal Gas Law • Boyle’s Law • At a constant temperature, pressure is inversely proportional to the volume • Charles’ Law • At a constant pressure, the temperature is directly proportional to the volume • Gay-Lussac’s Law Ideal Gas Properties • At a constant volume, the pressure is directly proportional to the temperature • These 3 laws are summarized by the Ideal Gas Law: • R =universal gas constant= 8.31 J/molK = 0.0821 Latm/molK (P = absolute pressure, T = temp. in Kelvin) (note that if n = constant, PV/T = constant)

20. CQ2: If the volume of an ideal gas is doubled while its temperature is quadrupled, what happens to the pressure of the gas? • It remains the same. • It decreases by a factor of 2. • It decreases by a factor of 4. • It increases by a factor of 2. • It increases by a factor of 4.

21. Example Problem #10.32 A tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.20 atm? Solution (details given in class): 884 balloons

22. CQ3: Interactive Example Problem #10.35 A weather balloon is designed to expand to a maximum radius of 20 m at its working altitude, where the air pressure is 0.030 atm and the temperature is 200 K. If the balloon is filled at atmospheric pressure and 300 K, what is its radius at liftoff? • 4.2 m • 7.1 m • 18 m • 49 m • 358 m