# Week 20 (Jan. 8 - 12)

Key Topics:
temperature measurement, thermometry, thermal expansion, ideal gasses
Topics: The zeroth law of thermodynamics; thermometry; practical and absolute temperature scales; constant volume gas thermometry; ice, steam and triple points of water; Fahrenheit, Celsius and Kelvin temperature scales; thermal expansion coefficient; Boyle's and Charles' Laws; ideal gas law

Lab:

Homework Problems: The following problems should be finished and submitted electronically by Tuesday, January 16 at noon.

1. Short essay questions for class discussion:
• In principle, any gas can be used for a constant volume thermometer. Why can you not use oxygen below 15K? What gas might you use?
• Metal lids to glass jars can often be loosened by running hot water over them. How is this possible?
• Why should the amalgam used in dental fillings have the same average coefficient of thermal expansion as a tooth? What would occur if it didn't?
• A mass is suspended from a rubber band. When the rubber band is heated with a hair drier, the rubber band shrinks and the mass is lifted. What does this imply about the coefficient of linear expansion of rubber?
• Explain why a column of mercury in a glass thermometer first descends then rises when placed in a beaker of hot water.
• Markings to indicate length are placed on a steel tape in a room that has a temperature of 22 deg. C. Are measurements made on a warm day, when the temperature is 27 deg. C too long, too short, or accurate? Explain.
• The suspension of a pendulum clock is made of brass. When the temperature increases, does the period of the clock increase, decrease or remain the same? Explain.
• Why don't ponds freeze all the way to the bottom in the winter?
2. A constant volume gas thermometer is calibrated in dry ice (solid CO2 has a temperature of -80.0 deg. C) and in boiling ethyl alcohol (78.0 deg. C). The two pressures are 0.900 atm and 1.635 atm.
• What value of absolute zero does the calibration yield?
• What is the pressure at the freezing point of water?
• The boiling point of water?
3. A substance is heated from -12 deg. F to 150 deg. F. What is the change in temperature on the Celsius scale? The Kelvin scale?
4. A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0 deg. C. It is completely filled with turpentine, and then warmed to 80.0 deg. C.
• How much turpentine overflows?
• If it is then cooled back to 20.0 deg. C, how far below the cylinder's rim is the turpentine surface?
5. An air bubble originating from a deep sea diver has a radius of 5.0 mm at some depth h. When the bubble reaches the surface of the water, it has a radius of 7.0 mm. Assuming the temperature of the air in the bubble remains constant, determine
• the depth h of the diver
• the absolute pressure at this depth
6. Optional: A steel guitar string with a diameter of 1.00 mm is stretched between supports 80.0 cm apart. The temperature is 0.0 deg. C. The young's modulus of steel is 20e10 N/m^2 and the coefficient of linear is expansion is 11e-6 per deg. C.
• find the mass per unit length of the string (assume the density of steel is 7.86e3 kg/m^3).
• if the fundamental frequency f oscillation is 200 Hz, what is the tension in the string?
• If the temperature is raised to 30.0 deg. C, find the tension and the fundamental frequency.
General College Physics