Module 3 - Thermodynamics. Thermodynamics. Measuring Temperatures. Temperature and Thermal Equilibrium

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Susan Byrd
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1 Thermodynamics From the Greek thermos meaning heat and dynamis meaning power is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. Thermodynamics describes how systems respond to changes in their surroundings. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, cell biology, biomedical engineering, and materials science to name a few. The starting point for most thermodynamic considerations are the laws of thermodynamics, which postulate that energy can be exchanged between physical systems as heat or work. Module 3 - Thermodynamics Chapter 17 Temperature, Thermal Equilibrium, Expansion, Stresses Ideal Gases Chapter 18 Molecular Basis of Thermodynamics Vapor Pressure, Humidity, Mean Free Path, Diffusion Chapter 19 Heat 1 st Law of Thermodynamics Chapter 20 Cycles Engines 2 nd Law of Thermodynamics - Entropy Wikipedia: Temperature and Thermal Equilibrium The zeroth law of thermodynamics: If two systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with one another. If two thermal systems are in thermal equilibrium with one another, then they have the same temperature. Temperature is a way of determining (measuring?) thermal equilibrium Two systems have the same temperature They are in thermal equilibrium Two systems have different temperatures The are NOT in thermal equilibrium Measuring Temperatures Thermometer: a device that measures temperature quantitatively Minimal effect on system being measured Good contact with system being measured Reproducible and easily read scale Properties useful for thermometry: Thermal expansion of fluids and solids Pressure of gases Reflective properties Electric and magnetic properties Color 1

Some Thermometers Temperature Scales Fahrenheit: t F = 32 at freezing point of water t F = 212 at boiling point Celsius: t C = 0 at freezing point of water t C = 100 at boiling point T T 5 9 ( C) =

coefficient of volume expansion (β) instead (as length is not well-defined): ΔV β = 1 V o ΔT OR ΔV = VoβΔT You want to insert an aluminum rod, which at 20.0 C has a radius of 1.

2 Some Thermometers Temperature Scales Fahrenheit: t F = 32 at freezing point of water t F = 212 at boiling point Celsius: t C = 0 at freezing point of water t C = 100 at boiling point T T 5 9 ( C) = [ T ( F ) 32] 9 5 ( F ) = T ( C) + 32 Thermal Expansion Solids expand when temperature increases; describe by coefficient of thermal expansion (α): ΔL α = 1 L o ΔT OR ΔL = LoαΔT For fluids, use coefficient of volume expansion (β) instead (as length is not well-defined): ΔV β = 1 V o ΔT OR ΔV = VoβΔT You want to insert an aluminum rod, which at 20.0 C has a radius of cm into a copper tube which has a radius of cm at the same temperature. You decide to put both of them in the refrigerator. At what temperature will the rod just fit if both are cooled to the same temperature? 2

3 Thermal Stress Induced stress when the material does not freely expand or contract due to a temperature change The material is restricted in some manner ΔL = LoαΔT An aluminum rod 1.50 m long and with a cross-sectional area of m 2 is heated to 300 C and clamped at both ends. The temperature of the rod is then lowered 20.0 C. As a result, the rod would normally contract, but it is prevented from doing so by the clamps. What is the tension in the rod? For aluminum, the coefficient of thermal expansion is o C -1 and the value of Young's modulus is Pa. But σ = Eε F A ΔL = E L o σ = F A LoαΔT = E L o = EαΔT 3

4 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? Freezing Cold 1) yes, at 0 C 2) yes, at -273 C 3) yes, at 0 K 4) 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). Thermometers 1) the mercury contracts before the You may notice that if a glass contracts mercury-in-glass thermometer 2) the glass contracts before the is inserted into a hot liquid, the mercury contracts mercury column first drops, 3) the mercury contracts before the and then later starts to rise (as glass expands you expect). How do you 4) the glass expands before the mercury expands explain this drop? 5) the mercury expands before the glass contracts The hot liquid touches the glass first, so initially the glass expands slightly. This increases the volume inside the glass, and so the mercury level drops slightly. Once the mercury heats up, it begins to expand and then the characteristic rise in the mercury column follows, indicating the increase in temperature that you expected to measure. Glasses Steel Expansion I Two drinking glasses are stuck, one inside the other. How would you get them unstuck? 1) run hot water over them both 2) put hot water in the inner one 3) run hot water over the outer one 4) run cold water over them both 5) break the glasses A steel tape measure is marked such that it gives accurate length measurements at room temperature. If the tape measure is used outside on a very hot day, how will its length measurements be affected? 1) measured lengths will be too small 2) measured lengths will still be accurate 3) measured lengths will be too big Running hot water only over the outer glass will allow the outer one to expand, while the inner glass remains relatively unchanged. This should loosen the outer glass and free it. The tape measure will expand, so its markings will spread out farther than the correct amount. When it is laid down next to an object of fixed length, you will read too few markings for that given length, so the measured length will be too small. Page 1 1

Metals such as brass expand when heated. The thin brass plate in the movie has a circular hole in its center. When the plate is heated, what will happen to the hole?

5 Metals such as brass expand when heated. The thin brass plate in the movie has a circular hole in its center. When the plate is heated, what will happen to the hole? Steel Expansion II 1) gets larger 2) gets smaller 3) stays the same 4) vanishes A steel ring stands on edge with a rod of some material inside. As this system is heated, for which of the following rod materials will the rod eventually touch the top of the ring? Steel Ring I 1) aluminum 2) steel 3) glass 4) aluminum and steel 5) all three Imagine drawing a circle on the plate. This circle will expand outward along with the rest of the plate. Now replace the circle with the hole, and you can see that the hole will expand outward as well. Note that the material does NOT expand inward to fill the hole!! expansion Quartz Glass Steel Al Hg Coefficient of volume expansion β (1/ C ) Aluminum is the only material that has a larger β value than the steel ring, so that means that the aluminum rod will expand more than steel ring. Thus, only in that case does the rod have a chance of reaching the top of the steel ring. Air Steel Ring II Grandfather Clock You want to take apart a couple of aluminum parts held together by steel screws, but the screws are stuck. What should you do? 1) heat the thing up 2) cool the thing down 3) blow the thing up A grandfather clock uses a brass pendulum to keep perfect time at room temperature. If the air conditioning breaks down on a very hot summer day, how will the grandfather clock be affected? 1) clock will run slower than usual 2) clock will still keep perfect time 3) clock will run faster than usual Quartz Glass Steel Al Coefficient of volume expansion β (1/ C ) Since aluminum has a larger β 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. Hg Air The pendulum will expand, so its length will increase. The period of a pendulum depends on the length as shown below, so the period will also increase. Thus, the clock will run slow. T = 2π ( L / g ) Follow-up: Roughly by how much will it run slower? Page 2 2

Module 3 - Thermodynamics. Thermodynamics. Measuring Temperatures. Temperature and Thermal Equilibrium

Module 3 - Thermodynamics. Thermodynamics. Measuring Temperatures. Temperature and Thermal Equilibrium Thermodynamics From the Greek thermos meaning heat and dynamis meaning power is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic