Chapter 10: hermal Physics hermal physics is the study of emperature, Heat, and how these affect matter. hermal equilibrium eists when two objects in thermal contact with each other cease to echange energy. Zeroth Law of hermodynamics (law of equilibrium): If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other. Objects in thermal equilibrium with each other are at the same temperature. hermometers and emperature Scales constant volume gas thermometer Any physical property which changes sensitively with the temperature can be used as thermometer. For eample, the pressure of gas at a constant volume is an indicator of temperature. Celsius and Fahrenheit are artificially defined temperature scales. he absolute temperature (Kelvin) scale defines an absolute zero as a lower bound for physical processes. C + 7.15
emperature Scales C 7.15 F 9 5 C + hermal Epansion hermal epansion is due to the change of average spacing between atoms as temperature changes. he length of a solid object (with an initial length L 0 at temperature 0 ) changes by ΔL for a change Δ in temperature: ΔL α L 0 Δ L - L 0 ΔL α L 0 ( - 0 ) α is the coefficient of linear epansion. he volume change of an object with a change in temperature is ΔV β V 0 Δ β is the coefficient of volume epansion. Usually, β α.
hermal Epansion Eample Problems 18. A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.700 m when the temperature is 1. C, what is the measured length when the temperature rises to 9.4 C? (Note: Don t neglect the epansion of the steel tape.) 6. A constant-volume gas thermometer is calibrated in dry ice ( 80.0 C) and in boiling ethyl alcohol (78.0 C). he two pressures are 0.900 atm and 1.65 atm. (a) What value of absolute zero does the calibration yield? (b) What pressures would be found at the freezing and boiling points of water? (Note that we have a linear relationship between P and as P A + B, where A and B are constants.)
Macroscopic Description of An Ideal Gas One mole of any substance contains as many particles as there are atoms in 1 g of the carbon-1 isotope. (Avogadro s number N A 6.0 10 ) An ideal gas is a collection of atoms or molecules that move randomly, eert no long-range forces on one another, and occupy a negligible fraction of the volume of their container. For any ideal gas: PV nr, where n is the number of moles, is the absolute temperature, the universal gas constant R 8.1 J/mol-K 0.081 L*atm / mol-k Macroscopic Description of An Ideal Gas PV nr he volume occupied by 1 mole of any gas at atmospheric pressure and at 0 o C is.4 L. (Equal volumes of gas at the same temperature and pressure contain the same number of molecules.) R N A k B PV nr N k B N: number of molecules; k B : Boltzmann s constant k B R / N A 1.8 10 J / K
he Kinetic heory of Gases Assumptions: 1. he number of molecules in the gas is large. However, the average separation of molecules is large compared with their dimensions.. he molecules obey Newton s law of motion, but as a whole they move randomly.. Molecules interact only through short-range forces during elastic collisions. 4. he molecules make elastic collisions with the walls. 5. All molecules in the gas are identical. he Kinetic heory of Gases Assume N molecules of an ideal gas are inside a cubic container of volume V (d V). Let s figure out the impulse eerted by one particular molecule in one collision with the wall at d. Δp mv ( mv ) mv How often does this molecule collide with this wall? Δt d / In unit time, the total impulse received by the wall from this molecule is Δp mv mv / d Δt d / v In unit time, the total impulse received by the wall from ALL HE MOLECULES is v Nm v / d
he Kinetic heory of Gases he average force received by the wall from the molecules is I F Nm v / d Δt F Nm v d P A d Because space is isotropic, PV 1 m v v 1 N ( m v ) k / B N V m v vz vy But we also know that PVNk B. herefore, 1 v emperature is a measure of average molecular speed KE total Molecular Interpretation of emperature 1 m v k 1 N ( m v ) U nr B Nk B nr v rms kb m R M Mawell velocity distribution N m f ( v) 4π kb π / mv kb v e For hydrogen molecules at R, the rms velocity ~ 1.9 km/s! GM E vesc 11. km / s R E
Problems 50. A vertical cylinder of crosssectional area 0.050 m is fitted with a tight-fitting, frictionless piston of mass 5.0 kg (Fig. P10.50). If there is.0 mol of an ideal gas in the cylinder at 500 K, determine the height h at which the piston will be in equilibrium under its own weight. 60. wo small containers of equal volume, 100 cm, each contain helium gas at 0 C and 1.00 atm pressure. he two containers are joined by a small open tube of negligible volume, allowing gas to flow from one container to the other. What common pressure will eist in the two containers if the temperature of one container is raised to 100 C while the other container is kept at 0 C? Chapter 10 Summary Zeroth law of thermodynamics. emperature scales hermal epansion Ideal gas Average (translational) kinetic energy per molecule: proportional to