THERMODYNAMICS

1. THERMODYNAMICS Day 6 of 9

2. Review of Temperature • A measure of the average kinetic energy of all the particles in an object

3. Thermal Expansion • When an object gets hotter, the internal molecules have an increase in kinetic energy, and the molecules start vibrating more and more. Since the molecules in a solid are essentially locked into position, this increase in movement causes them to space apart ever so slightly.

4. Thermal Expansion • Therefore, most materials expand when heated

5. Thermal Expansion • Objects can expand in: one dimension aka linear expansion two dimensions aka area expansion three dimensions aka volume expansion

6. Linear Expansion • Change in length = (coefficient alpha) x (original length) x (temperature change) ΔL=αL0ΔT

7. Area Expansion • Change in area= 2 x (coefficient alpha) x (original area) x (temperature change) ΔA =2αA0ΔT

8. Volume Expansion • Volume expansion is similar, except that it is relevant for liquids and gases as well as solids. • Change in Volume = (coefficient beta) x (original volume) x (temperature change) ΔV =βV0ΔT

10. Example • Ernesto is knitting his wife a sweater in his 18°C air-conditioned living room with 0.30 meter long aluminum knitting needles, when he decides to knit outside in the 27°C air. How much will the knitting needles expand in length when Ernesto takes them outside?(αaluminum = 24 x 10-6 °C-1)

11. Exercise 1 • A long piece of iron that is 2.1 meters long at room temperature (25°C) is heated uniformly along its entire length until its temperature reaches 950°C. How much longer is the bar at the higher temperature?(The coefficient of linear expansion of iron is 1.2 x 10-5 °C-1)

12. Exercise 2 • Selena has a fire in the fireplace to warm her 20.0°C apartment. She realizes that she left the iron poker in the fire. How much longer is the iron poker if the fire gets up to 436°C?(The coefficient of linear expansion of iron is 1.2 x 10-5 °C-1)

13. ConcepTest 13.3 Thermometers 1) the mercury contracts before the glass contracts 2) the glass contracts before the mercury contracts 3) the mercury contracts before the glass expands 4) the glass expands before the mercury expands 5) the mercury expands before the glass contracts You may notice that if a mercury-in-glass thermometer is inserted into a hot liquid, the mercury column first drops, and then later starts to rise (as you expect). How do you explain this drop?

14. ConcepTest 13.3 Thermometers 1) the mercury contracts before the glass contracts 2) the glass contracts before the mercury contracts 3) the mercury contracts before the glass expands 4) the glass expands before the mercury expands 5) the mercury expands before the glass contracts • You may notice that if a mercury-in-glass thermometer is inserted into a hot liquid, the mercury column first drops, and then later starts to rise (as you expect). How do you explain this drop? 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. Follow-up: Is it possible to have the mercury first rise and later drop?

15. ConcepTest 13.4 Glasses 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 Two drinking glasses are stuck, one inside the other. How would you get them unstuck?

16. ConcepTest 13.4 Glasses 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 Two drinking glasses are stuck, one inside the other. How would you get them unstuck? 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.

17. ConcepTest 13.5a Steel Expansion I 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

18. ConcepTest 13.5a Steel Expansion I 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 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.

19. ConcepTest 13.5b Steel Expansion II 1) gets larger 2) gets smaller 3) stays the same 4) vanishes 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?

20. expansion ConcepTest 13.5b Steel Expansion II 1) gets larger 2) gets smaller 3) stays the same 4) vanishes 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? 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!!