Chapter 17 Temperature and Heat

Measuring temperature There are many ways to measure temperature, but the two devices mentioned below take advantage of a gas or liquid sample which expands if heat is added and contracts if heat is removed. A cylinder of gas will show pressure rise if volume is kept constant. A small container of liquid will see the liquid increase in volume as temperatures rise. Mercury was chosen “early on” because it’s so dense, a small volume can record large temperature ranges.

The zeroth law of thermodynamics Simply stated? “Heat will always travel from a hot reservoir to a cold one without outside energy forcing an unnatural transfer.”

Q17.1 The illustration shows a thermometer that uses a column of liquid (usually mercury or ethanol) to measure air temperature. In thermal equilibrium, this thermometer measures the temperature of A. the column of liquid. B. the glass that encloses the liquid. C. the air outside the thermometer. D. both A. and B. E. all of A., B., and C.

A17.1 The illustration shows a thermometer that uses a column of liquid (usually mercury or ethanol) to measure air temperature. In thermal equilibrium, this thermometer measures the temperature of A. the column of liquid. B. the glass that encloses the liquid. C. the air outside the thermometer. D. both A. and B. E. all of A., B., and C.

The coldest we can ever get? Early experiments observed changes in pressure or volume as temperature changed. It was noticed that the linear trends lead to a consistent lowest temperature that we call “absolute zero”—labeled 0K after Lord Kelvin. Coldest temperature in experiment: 4.5 x 10-10 K

Conversions are expected Values on the temperatures scales (Fahrenheit, Centigrade/Celsius, and Kelvin) may be readily interconverted. Physics professors will want values to eventually be in Kelvins because that’s the form in SI units (and Fahrenheit is dumb).

Q17.2 A sample of a low-density gas is initially at room temperature and has pressure p0. The gas is warmed at constant volume until the pressure is 2p0. Compared to the initial Celsius temperature of the gas, the final Celsius temperature is A. greater by a factor of more than 2. B. greater by a factor of 2. C. greater by a factor between 1 and 2. D. the same. E. less.

A17.2 A sample of a low-density gas is initially at room temperature and has pressure p0. The gas is warmed at constant volume until the pressure is 2p0. Compared to the initial Celsius temperature of the gas, the final Celsius temperature is A. greater by a factor of more than 2. B. greater by a factor of 2. C. greater by a factor between 1 and 2. D. the same. E. less.

Thermal expansion—linear A change in length will accompany a change in temperature. The size of the change will depend on the material.

Changing temperature changes atomic spacing Molecules can be visualized as bedsprings and spheres. More heat (higher temperatures) is reflected by the motion of the atoms relative to each other. See Figure 17.9 below.

Coefficients of expansion

Q17.3 A solid object has a hole in it. Which of these illustrations more correctly shows how the size of the object and the hole change as the temperature increases? #1 #2 A. illustration #1 B. illustration #2 C. The answer depends on the material of which the object is made. D. The answer depends on how much the temperature increases. E. Both C. and D. are correct.

A17.3 A solid object has a hole in it. Which of these illustrations more correctly shows how the size of the object and the hole change as the temperature increases? #1 #2 A. illustration #1 B. illustration #2 C. The answer depends on the material of which the object is made. D. The answer depends on how much the temperature increases. E. Both C. and D. are correct.

Thermal changes in material length and volume You have an aluminum cube that is too tight to fit into a square hole. If it has 5cm on each side at room temperature (22°C), what dimensions does the cube have if you put it into an ice cooler ? Coefficient of linear expansion is 2.4 x 10-5 and coefficent of volume expansion is 7.2 x 10-5 for aluminum.

Thermal expansion we see constantly Water is interesting. There are no other liquids that expand to become less dense as a solid than they are as a liquid. This is fortunate, if lakes were to freeze and dense ice sink to the bottom, everything in the water would die as the liquid became solid from the bottom up. Thermal expansion joints allow roads to expand and contract without any stress to the material used to build.

James Joule and the mechanical equivalent of heat Joule knew a mass above the ground had potential energy. He dropped an object on a cord, turning a paddle in water monitored by a very accurate thermometer. His conclusion was to connect energy conservation (potential and kinetic) to heat as a third form observed.

Specific heat A specific heat value reveals how much temperature will change when a given amount of a substance absorbs a given amount of heat. Water is a “benchmark” as one ml of water will absorb 1 cal of heat to raise its temperature by 1oC.

Specific heat values

Q17.3.5 You put 1 kg of the following materials on a bunsen burner. Which one’s temperature rises the least? A. Aluminum, c = 910 J/kg K B. Berillium, c = 1970 J/kg K C. Copper, c = 390 J/kg K D. Water, c = 4190 J/kg K

A17.3.5 You put 1 kg of the following materials on a bunsen burner. Which one’s temperature rises the least? A. Aluminum, c = 910 J/kg K B. Berillium, c = 1970 J/kg K C. Copper, c = 390 J/kg K D. Water, c = 4190 J/kg K

Phase changes and temperature behavior A solid will absorb heat according to its heat capacity, becoming a hotter solid. At the melting point, a solid will absorb its heat of fusion and become a liquid. An equilibrium mixture of a substance in both its liquid and solid phases will have a constant temperature. A cold liquid will absorb heat according to its heat capacity to become a hotter liquid. At the boiling point, a liquid will absorb its heat of vaporization and become a gas. An equilibrium mixture of liquid and gas will have a constant temperature. A cold gas can absorb heat according to its heat capacity and become a hotter gas.

Heats of Fusion and Heats of Vaporization

Q17.4 You wish to increase the temperature of a 1.00-kg block of a certain solid substance from 20°C to 25°C. (The block remains solid as its temperature increases.) To calculate the amount of heat required to do this, you need to know A. the specific heat of the substance. B. the molar heat capacity of the substance. C. the heat of fusion of the substance. D. the thermal conductivity of the substance. E. more than one of the above

A17.4 You wish to increase the temperature of a 1.00-kg block of a certain solid substance from 20°C to 25°C. (The block remains solid as its temperature increases.) To calculate the amount of heat required to do this, you need to know A. the specific heat of the substance. B. the molar heat capacity of the substance. C. the heat of fusion of the substance. D. the thermal conductivity of the substance. E. more than one of the above

Using well-behaved water to measure other systems Because water is a good thermal sink, is readily available, and reproducibly absorbs 4.184 J for every gram to rise in temperature by 1oC, it is often used to measure another object’s change in heat energy by comparison. For example, an unknown metal might be massed, raised to a known temperature (say to 100oC in a boiling water bath), then added to a known amount of cold water. The resulting change in the temperature of the water will allow heat absorbed to be calculated and then the heat capacity of the unknown metal.

Hot pot A heavy copper pot of mass 2 kg is at temperature of 150C. You pour 0.1 kg of water at 25C into the pot then quickly close the lid so no steam can escape. Find the final temperature of the pot and its contents and determine the phase (liquid or gas) of the water. Assume no heat is lost to the surroundings.

Why, and how well, do materials transfer heat? Conduction: heat transfer within a body or between two bodies in contact. Convection: heat transfer through movement of mass from one place to another Radiation: heat transfer by electromagnetic radiation

Conduction of heat I You bring a cooler to the beach to keep some tasty beverages cold. The cooler has a total wall area of 0.8 m2 and a wall thickness of 2.0 cm. It is filled with ice, water and your tasty beverage at 0C. What is the rate of heat flow into the cooler if the outside wall is at 30C? How much ice melts in 8 hours?

Conduction of heat III Consider Example 17.14. There are variations of the metal bar problem. Figure 17.27 below illustrates the problem.

Convection of heat Heating by moving large amounts of hot fluid, usually water or air. Figure 17.28 at right illustrates heat moving by convection.

Radiation of heat Infrared lights, hot metal objects, a fireplace, standing near a running furnace … these are all objects heating others by broadcast of EM radiation just lower in energy than visible red. Consider Example 17.15. Consider Example 17.16.