Thermal Systems & Temperature Lecturer: Professor Stephen T. Thornton

Reading Quiz Reading Quiz A) cylinder A B) cylinder B C) both the same D) it depends on temperature T Two identical cylinders at the same temperature contain the same gas. If A contains three times as much gas as B, which cylinder has the higher pressure?

PV = nRT Ideal gas law: PV = nRT Solve for pressure: the larger value of n For constant V and T, the one with more gas (the larger value of n) has the higher pressure P. Reading Quiz Reading Quiz A) cylinder A B) cylinder B C) both the same D) it depends on temperature T Two identical cylinders at the same temperature contain the same gas. If A contains three times as much gas as B, which cylinder has the higher pressure?

Last Time Simple pendulum Physical pendulum Damped and forced oscillations

Today Thermal systems, reservoirs Temperature Heat flow Thermometers Temperature scales Low temperatures Look at P ~ T Thermal expansion

Begin Thermodynamics We understand that you have already studied much of this material in chemistry during high school and college. We will mostly emphasize the fundamental, underlying principles which depend on the physical laws of nature. Mention waves and sound.

A thermal system is a physical system having temperature-dependent properties. A piston and cylinder full of hot steam is a thermal system. If we pour hot water into a bucket of cold water, the temperature eventually is the same throughout the system. We say they have reached thermal equilibrium. The system is then at a single, constant temperature.

A thermal reservoir (or heat bath) is a thermal system so large that it keeps a constant temperature when it interacts with other systems. A large lake is a thermal reservoir. The outside atmosphere is a thermal reservoir. Your kitchen sink full of water is not a thermal reservoir. When systems come into thermal contact with each other, they can exchange energy.

Temperature, heat concepts  Temperature is not the same thing as heat.  Temperature refers to how “hot” or “cold” something is.  Temperature is related to the internal energy or thermal energy of a system.  Heat refers to a flow of energy.  There is no such concept as absolute heat. Heat flow is more appropriate.

Heat flow is the energy transferred between objects because of a temperature difference. We speak of “heat flow” or “transfer of heat”. Remember that there is no such thing as “absolute heat”.

0 th Law of Thermodynamics Two objects in thermal equilibrium with a third object are also in thermal equilibrium with each other. Seems trivial, but it is important when we begin doing experiments.

Thermometers It is not so easy to build good thermometers. Criteria:  Must be small enough to not affect system being measured.  Must have good thermal contact.  Reproducible, easily read, safe, widely available.  Accurate over wide range of temperatures.

Comparison of Temperature Scales

Temperature Scale Conversions Important temperatures: Ice 0 0 C 32 0 F 273 K Boiling water C F 373 K

Kelvin temperature Because temperature is a measure of the energy of a thermal system, it makes sense to have zero (0) as the lowest possible temperature. 1 C 0 temperature change = 1 K change At 0 K, most motion stops.

It turns out that –40°C is the same temperature as –40°F. Is there a temperature at which the Kelvin and Celsius scales agree? A) yes, at 0°C B) yes, at − 273°C C) yes, at 0 K D) no Conceptual Quiz

It turns out that –40°C is the same temperature as –40°F. Is there a temperature at which the Kelvin and Celsius scales agree? A) yes, at 0°C B) yes, at − 273°C C) yes, at 0 K D) no The Celsius and Kelvin scales differ only by an offset, which is 273 degrees. Therefore, a temperature on one scale can never match the same numerical value on the other scale. The reason that such agreement is possible for Celsius and Fahrenheit is the fact that the actual degree units have different sizes (recall the previous question). Conceptual Quiz

Do LN 2 demos Strange things happen at low temperatures. Liquid nitrogen temperature: F C 77 K

Constant-Volume Gas Thermometer Adjust right hand side so mercury is always at same height. Volume is constant. pV = nRT P gas = P atm +  gh. Change temperature, readjust pressure

Do absolute zero demo. See next slide while demonstrating. I hope you are able to do this lab at UVa.

Take data for several gases at different temperatures. Extrapolate straight line curves to find 0 K. In lab you do this for He gas for different numbers of moles. Show that P ~ T at constant volume. Intercepts absolute zero.

Consider a rod of length at temperature T 0. When heated it expands (where  = coefficient of linear expansion [unit 0 C -1 )] Most substances expand when heated. We have all seen expansion joints in concrete sidewalks, on highways, on steel bridges, etc.

Do demos of linear expansion. Start bolt cracker Do bimetallic strip – see next slide Ring and ball – do later

A Bimetallic Strip Do bimetallic strip demo. Here metal B has a larger coefficient of linear expansion. Some thermostats use bimetallic strips.

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Copyright © 2009 Pearson Education, Inc. Thermal Expansion Note that metals expand more than most materials. Gases expand more than liquids, which expand more than solids.

Conceptual Quiz: We sometimes pour hot water on a metal lid that seems to be stuck on a glass jar. Why do we do this? A) Because glass expands more than the lid, which will loosen the lid. B) Because the junk between the lid and the glass will melt and flow out. C) Because the metal lid expands more than the glass, which will loosen the lid. D) Because I once saw it done on television, and it worked.

Answer: C The thermal expansion coefficients of metal are much greater than that of glass. The hot water causes the metal lid to expand much more than the glass jar, which will loosen the lid.

Conceptual Quiz: Consider a metal plate with a circular hole cut somewhere inside. If the entire plate is then heated, how does the size of the hole change? A) Becomes larger B) Becomes smaller C) No change in size D) Depends on the metal

Answer : A Imagine drawing a circle on the plate, but without the hole being cut. In this case the entire metal plate expands. So therefore would your drawn circle, and so therefore would the hole itself.

Do ball through ring demo. Heat ring and see if ball goes through.

Volume Expansion If we heat solid cube, it all expands. If we separate cubes and heat, both the small cube and the hole in the large cube expand. The hole gets larger and cube still fits.

Conceptual Quiz       Coefficient of volume expansion  (1/°C ) GlassHgQuartzAir   AlSteel A) heat the thing up B) cool the thing down C) blow the thing up You want to take apart a couple of aluminum parts held together by steel screws, but the screws are stuck. What should you do?

aluminum has a larger  valuealuminum expands more than steel aluminum holes will expand faster than the steel screws Since aluminum has a larger  value, that means aluminum expands more than steel. Thus, by heating the part, the aluminum holes will expand faster than the steel screws and the screws will come loose. Conceptual Quiz       Coefficient of volume expansion  (1/°C ) GlassHgQuartzAir   AlSteel A) heat the thing up B) cool the thing down C) blow the thing up You want to take apart a couple of aluminum parts held together by steel screws, but the screws are stuck. What should you do?