1. PHY 231 1 PHYSICS 231 Lecture 25: Viscosity (ch.9) and Temperature (ch. 10) Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom

2. PHY 231 2 Applications of Bernoulli’s law: the golf ball P1P1 P2P2 Neglecting the small change in height between the top and bottom of the golf ball: P 1 +½  v 1 2 = P 2 +½  v 2 2 P 1 -P 2 = ½  (v 2 2- v 1 2 ) P1P1 P2P2 P 1 -P 2 = ½  (v 2 2- v 1 2 )=0 v 2 =v 1 No pressure difference, no lift P 1 -P 2 = ½  (v 2 -v) 2 -(v 1 + v) 2 =0 P 2 >P 1 so: Upward force: the ball goes higher and thus travels faster

3. PHY 231 3 Viscosity Viscosity: stickiness of a fluid One layer of fluid feels a large resistive force when sliding along another one or along a surface of for example a tube.

4. PHY 231 4 Viscosity Contact surface A fixed moving F=  Av/d  =coefficient of viscosity unit: Ns/m 2 or poise=0.1 Ns/m 2

5. PHY 231 5 Poiseuille’s Law How fast does a fluid flow through a tube? Rate of flow Q=  v/  t=  R 4 (P 1 -P 2 ) 8L8L (unit: m 3 /s)

6. PHY 231 6 Example PP=10 6 Pa P=10 5 Pa Flow rate Q=0.5 m 3 /s Tube length: 3 m  =1500E-03 Ns/m 2 What should the radius of the tube be? Rate of flow Q=  R 4 (P 1 -P 2 ) 8L8L R=[8Q  L/(  (P 1 -P 2 ))] 1/4 =0.05 m

7. PHY 231 7 Chapter 10 Temperature R Potential Energy 0 R 2 atom/molecules -E min The curve depends on the material, e.g. E min is different for water and iron Kinetic energy ~ T

8. PHY 231 8 Solid (low T) R Potential Energy 0 Kinetic energy ~ T -E min The temperature (and thus kinetic energy) is so small that the atoms/molecules can only oscillate around a fixed position R min R min

9. PHY 231 9 Liquid (medium T) R Potential Energy 0 Kinetic energy ~ T -E min R min On average, the atoms/molecules like to stick together but sometimes escape and can travel far.

10. PHY 231 10 Gas (high T) R Potential Energy 0 Kinetic energy ~ T -E min R min The kinetic energy is much larger than E min and the atoms/molecules move around randomly.

11. PHY 231 11 What happens if the temperature of a substance is increased? R 0 Kinetic energy ~ T -E min R min =R ave (T=0) T=0: Average distance between atoms/molecules: R min R ave (T>0) > R min T>T o : The average distance between atoms/molecules is larger than R min : the substance expands

12. PHY 231 12 Temperature scales Conversions T celsius =T kelvin -273.5 T fahrenheit =9/5*T celcius +32 We will use T kelvin. If T kelvin =0, the atoms/molecules have no kinetic energy and every substance is a solid; it is called the Absolute zero-point. Kelvin Celsius Fahrenheit

13. PHY 231 13 Thermal expansion  L=  L o  T L0L0 LL T=T 0 T=T 0 +  T  A=  A o  T  =2   V=  V o  T  =3  length surface volume Some examples:  =24E-06 1/K Aluminum  =1.2E-04 1/K Alcohol  : coefficient of linear expansion different for each material

14. PHY 231 14 Thermal equilibrium Low temperature Low kinetic energy Particles move slowly High temperature High kinetic energy Particles move fast Thermal contact Transfer of kinetic energy Thermal equilibrium: temperature is the same everywhere

15. PHY 231 15 Zeroth law of thermodynamics If objects A and B are both in thermal equilibrium with an object C, than A and B are also in thermal equilibrium. There is no transfer of energy between A, B and C

16. PHY 231 16 Thermal expansion: an example In the early morning (T=30 o F=272.4K) a person is asked to measure the length of a football field with an aluminum measure and finds 109.600 m. Another person does the same in the afternoon (T=60 o F=289.1K) using the same ruler and finds 109.566 m. What is the coefficient of linear expansion of the ruler?  L=  L o  T so  =  L/(L 0  T)  T=16.7K L 0 =109.60  L=109.644-109.600=0.044 So:  =24E-06 1/K

17. PHY 231 17 A heated ring A metal ring is heated. What is true: a)The inside and outside radii become larger b)The inside radius becomes larger, the outside radius becomes smaller c)The inside radius becomes smaller, the outside radius becomes larger d)The inside and outside radii become smaller

18. PHY 231 18 Demo: bimetallic strips Application: contact in a refrigerator  top  bottom  top <  bottom if the temperature increases, The strip curls upward, makes contact and switches on the cooling.

19. PHY 231 19 Demo’s Bimetallic coil Expanding and contracting rod

20. PHY 231 20 Water: a special case Coef. of expansion is negative: If T drops the volume becomes larger Coef. Of expansion is positive: if T drops the volume becomes smaller Ice is formed (it floats on water)

21. PHY 231 21 Ice liquid ice  (g/cm 3 ) 1 0.917 Phase transformation Ice takes a larger volume than water!