1. Fluid Flow and Continuity Imagine that a fluid flows with a speed v 1 through a cylindrical pip of cross-sectional area A 1. If the pipe narrows to a cross- sectional area A 2, as in the right-hand portion of the Figure, the fluid will flow with a new speed, v 2. Any amount of fluid that passes point 1 in a given time,  t, must also flow past the point 2 in the same time. To find the mass of fluid passing point 1 in the time  t, note that the fluid moves through a distance v 1  t in this time. As a result, the volume of fluid going past point 1 is

2. Fluid Flow and Continuity the volume of fluid going past point 1 is Hence, the mass of fluid passing point 1 is Similarly, the mass passing point 2 in the same time, Equation of Continuity

3. Example 7: Spray I Water travels through a 9.6 cm diameter fire hose with a speed of 1.3 m/s. At the end of the hoe, the water flows out through nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle?

4. Physics 102 Part II Thermal Physics Moza M. Al-Rabban Professor of Physics mmr@qu.edu.qa Temperature and Heat Lecture 13 Temperature and Heat Lecture 13

5. Temperature and the Zeroth Law of Thermodynamics Heat is the energy transferred between objects because of a temperature difference. Therefore, when we say that there is a “transfer of heat” or a “ heat flow” from object A to object B, it means that the total energy of object A decreases and the total energy of object B increases.

6. Heat Definition: Flow of energy between two objects due to difference in temperature –Note: similar to WORK –Object does not “have” heat (it has energy)

7. Temperature How hot or cold an objects feels? Thermal Contact Two objects are in thermal contact if they can exchange energy by Heat (includes conduction) Electromagnetic radiation Energy is exchanged when there is a temperature difference Thermal contact does not have to also be physical contact Thermal Equilibrium Thermal equilibrium is a when two objects would not exchange energy by heat or electromagnetic radiation if they were placed in thermal contact. The transfer of heat ceases. Two objects in thermal equilibrium are at the same temperature Objects at different temperatures are not in thermal equilibrium They will exchange energy if brought into thermal contact Zeroth Law of Thermodynamics If objects A and B are in thermal equilibrium with a third object C Then A and B are in thermal equilibrium with each other

9. Thermometers Make use of physical properties that change with temperature Many physical properties can be used –volume of a liquid –length of a solid –pressure of a gas held at constant volume –volume of a gas held at constant pressure –electric resistance of a conductor –color of a very hot object

10. Celsius Scale Temperature of an ice-water mixture is defined as 0º C –This is the freezing point of water Temperature of a water-steam mixture is defined as 100º C –This is the boiling point of water Distance between these points is divided into 100 segments There is no upper limit to the value a temperature may have. There is a lower limit, however. For the Celsius scale, it is -273.15  C. Temperature scales A temperature of five degrees is 5  C (five degrees Celsius) A temperature change of five degrees is 5 C  ( five Celsius degrees)

11. The Fahrenheit Scale Temperature of an ice-water mixture is defined as 32º F –This is the freezing point of water Temperature of a water-steam mixture is defined as 212º C –This is the boiling point of water Distance between these points is divided into 180 segments Note that the Fahrenheit scale has : Different zero than the Celsius scale Different “size” for its degree. The Fahrenheit degrees are smaller by factor of 100/180 = 5/9

12. Conversion between Degrees Celsius and Degrees Fahrenheit Conversion between Degrees Fahrenheit and Degrees Celsius

13. Example:1 Temperature Conversions (a)On a fine spring day you notice that temperature is 75 F. What is the corresponding temperature on the Celsius scale? (b) If the temperature on a brisk winter morning is – 2.0 C, what is the corresponding Fahrenheit temperature? Part (a) Part (b)

14. Absolute Zero All gases extrapolate to the same temperature at 0 pressure This temperature is absolute zero Temperature readings are nearly independent of the gas Pressure varies with temperature when maintaining a constant volume

15. Example 2: It’s a Gas The gas in a constant-volume gas thermometer has a pressure of 80.0 kPa at 0.00 C. Assuming ideal behavior, as in the Figure, what is the pressure of this gas at 105 C? 1.Calculate the rate at which pressure increases for this gas: 2. Multiply this rate by the temperature change from -273.15 C to 105 C:

16. Kelvin Scale When the pressure of a gas goes to zero, its temperature is –273.15º C This temperature is called absolute zero This is the zero point of the Kelvin scale –273.15º C = 0 K To convert:

17. Modern Definition of Kelvin Scale Defined in terms of two points –Agreed upon by International Committee on Weights and Measures in 1954 First point is absolute zero Second point is the triple point of water –Triple point is the single point where water can exist as solid, liquid, and gas Same temperature and pressure Occurs at 0.01º C and P = 4.58 mm Hg

18. A comparison of temperature scales

19. Question You measure your body temperature with a thermometer calibrated in degrees Kelvin, 98 F. Convert it to Kelvin temperature scale 1. 307 K 2. 310 K 3. 313 K 4. 317 K 98 o F ~ 37 o C ~ 310 o K

20. The thermal expansion of an object is a consequence of the change in the average separation between its constituent atoms or molecules At ordinary temperatures, molecules vibrate with a small amplitude As temperature increases, the amplitude increases This causes the overall object as a whole to expand Thermal Expansion

21. Linear Expansion

23. For small changes in temperature The coefficient of linear expansion, , depends on the material SI unit for  : –These are average coefficients, they can vary somewhat with temperature

24. Applications A bimetallic strip Thermometer Thermostat

25. Thermal Expansion joints

26. Area Expansion l Two dimensions expand

27. Question You are given a 4.000-cm diameter steel ball bearing and a brass plate with a 3.994-cm diameter hole at room temperature (20C). You are asked to squeeze the steel ball through the brass plate. You are allowed to increase or decrease the temperature of the two objects. However, they should both be at equal temperature at all times. What can you do to succeed? (  brass = 2 x 10-5 /C,  steel = 1 x 10-5 /C) Cool the ball and the plate. Heat the ball and the plate. You can never succeed.

30. Volume Expansion Three dimensions expand –For liquids, only coefficient of volume expansion exists

31. Example 3 Oil Spill A copper flask with a volume of 150 cm3 is filled to the brim with olive oil. If the temperature of the system is increased from 6.0 C to 31 C, how much oil spills from the flask? 1. Calculate the change in volume of the oil 2. Calculate the change in volume of the flask: 3. Find the difference in volume expansions. This is the volume of oil that spills out:

32. Special Properties of Water The density of water actually increases as the water is heated between 0 C and 4 C. Maximum density occurs near 4 C. The unusual behavior of water near 4 C.

33. End Of Lecture 13