Physics 13: 1-5 Gas Behavior
Text Reading: Giancoli, Physics - Principles with Applications, Chapter 13: 1-5
- 13.1: Brownian motion is the apparently random movements of small particles being jostled about. We use this observable phenomenon to explain the more difficult-to-observe situation of individual molecules and atoms in gases: in gases, these objects are in constant motion, colliding with one another.
- 13.2: Temperature measures how hot or cold something is. We use thermometers, usually graduated in centigrade (celsius) for scientific work, although the US still uses Fahrenheit. In each scale, the key points are the freezing point of water (32°F or 0°C) and the boiling point of water (212°F or 100°C). If we want to convert from one to the other, we have to look at both the offset (0 to 32) and the size of the degree (100 degrees vs. 212 degrees between freezing and boiling points).
To get from Fahrenheit to centigrade, we first adjust the offset, then adjust the size of the degree:
T°C = 5/9 (T°F - 32).
To get from centigrade to Fahrenheit, we first adjust size, then add in the offset:
T°F = 9/5 T°C + 32
Because both scales set a 0 point relative to freezing water, both allow for negative degree readings. A third scale, the Kelvin scale, must be used in situations (like the gas laws) where differences in temperatures are critical and we cannot have negative temperature readings. Kelvin measure temperatures from a calculated absolute zero value (= -273.15 °C), below which there is no negative Kelvin temperature.
- 13.3: The zeroth law of thermodynamics is so called because physicists felt that it was even more fundamental than the law of the conservation of energy, which was already designated as the "first law" of thermodynamics. The zeroth law states that two systems in thermal equilibrium with some third system (i.e., at the same temperature so that no heat flows between them), they must be in thermal equilibrium with each other. This is similar to the arithmetic rule that if A = C and B = C, A = B. Implicit in this rule is the concept that objects that are not in thermal equilibrium (i. e., are at different temperatures) will experience a heat flow from the hotter to the colder object until they reach the same temperature and are in thermal equilibrium.
- 13.4: When we add energy to a solid or liquid substance, we give its atoms and molecules the ability to vibrate harder from their rest state, causing some expansion. We can calculate thermal expansion ΔL for different substances from its original length L as a function of the change in temperature ΔT and a constant α that depends on the type of substance:
Thermal expansion: ΔL = αL0ΔT
The coefficient of expansion α must be experimentally determined, and changes for different temperatures. Values in tables are usually given for "Standard Conditions", or "Standard Temperature and Pressure" (STP), which are usually 20° C and 1 atm pressure, since these are the conditions that apply for a laboratory in a temperate zone near sea level.
Note that water does not follow the expected rules of expansion and contraction with temperature; as it drops from freezing (starting at 4°C) to freezing (0 °C), it actually expands as its molecules align to form water crystals. This has very important consequences for the survival of life in lakes where the surface freezes first and then insulates the lower levels of the lake with a floating ice cap.
- 13.5: Thermal stress occurs when a material undergoes temperature change but is constrained by the proximity of other materials. Examples are the blocks of concrete in a freeway, or iron I-beams in a building, or water caught in the cracks between rocks. As the material expands, it pushes on (and is pushed on) by its container. When water freezes, its expansion places thermal stress on the surrounding rocks, pushing them apart, widening crevices and creating new fissures.
- Converting temperatures:
- Linear thermal expansion (expansion in one dimension):
- Ideal Gas Law
Read the following weblecture before chat: Thermal Equilibrium
Use the simlation on phases to get a sense for how molecules behave as they acquire and lose heat energy.
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