Gas and Beyond 3/30/09
What’s Up Doc? • Today we complete one topic, quickly cover another and then begin to discuss resonance. Without this topic, musical instruments would not exist! • WebAssign is due tomorrow night. You should have been able to do all but the last two problems without today’s discussion. • Next Examination is APRIL 15th. • Taxes due as well.
If the atomic mass of neon is 20 amu, how much neon would be needed to have an Avogadro's number of neon atoms? • 20 amu • 10 grams • 20 grams • 20 kilograms
The two fixed points used to define the modern Fahrenheit temperature scale are those of • boiling water and a mixture of ice and salt. • the body and a mixture of ice and salt. • the body and freezing water. • boiling water and freezing water.
The Absolute Temperature ScaleTemperature • Assume that we have a quantity of ideal gas in a special container designed to always maintain the pressure of the gas at some constant low value. • When the volume of the gas is measured at a variety of temperatures, we obtain the graph below. If the line on the graph is extended down to the left, we find that the volume goes to zero at a temperature of −273°C (−459°F). Although we could not actually do this experiment with a real gas, this very low temperature arises in several theoretical considerations and is the basis for a new, more fundamental temperature scale. • The Kelvin temperature scale (after Lord Kelvin), also known as the absolutetemperaturescale, has its zero at −273°C and the same-size degree marks as the Celsius scale. The difference between the Celsius and Kelvin scales is that temperatures are 273 degrees higher on the Kelvin scale. Water freezes at 273 K and boils at 373 K.
The Absolute Temperature ScaleTemperature • It is true that these various scales (F,C) are equivalent because conversions can be made between them. However, the absolute temperature scale has a greater simplicity for expressing physical relationships. • In particular, the relationship between the volume and temperature of an ideal gas is greatly simplified using absolute temperatures. The volume of an ideal gas at constant pressure is proportional to the absolute temperature. • This means that if the absolute temperature is doubled while keeping the pressure fixed, the volume of the gas doubles. • The volume of an ideal gas at constant pressure can be used as a thermometer. All we need to do to establish the temperature scale is to measure the volume at one fixed temperature. • Of course, thermometers must be made of real gases. But real gases behave like the ideal gas if the pressure is kept low and the temperature is well above the temperature at which the gas liquefies.
The Absolute Temperature ScaleTemperature • This new scale also connects the microscopic property of atomic speeds and the macroscopic property of temperature. • The absolute temperature is directly proportional to the average kinetic energy of the gas particles. • This means that if we double the average kinetic energy of the particles, the absolute temperature of a gas doubles. • Remember, however, that the average speed of the gas particles does not double, because the kinetic energy depends on the square of the speed.
Thunker: Temperature • When you wake, the temperature outside is 40°F, but by noon it is 80°F. Why is it not reasonable to say that the temperature doubled?
Convert 0C to 0K 0C 273 degrees width 0K=0C + 2730
The Ideal Gas Law • The three macroscopic properties of a gas—volume, temperature, and pressure—are related by a relationship known as the ideal gas law. • This law states that where P is the pressure, V is the volume, n is the number of moles, T is the absolute temperature, and R is a number known as the gas constant. R = 8.314472 J·mol−1·K−1
UNITS R = 8.314472 J·mol−1·K−1
A volume of 150 cm3 of an ideal gas has an initial temperature of 20°C and an initial pressure of 1 atm. What is the final pressure if the volume is reduced to 120 cm3 and the temperature is raised to 40°C? P=1.34 atm
WebAssign Hint:For this HW (#10), assume T=constant A helium bottle with a pressure of 100 atm has a volume of 2 L. How many balloons can the bottle fill if each balloon has a volume of 1 L and a pressure of 1.45 atm?
Which of the following statements is true for an ideal gas? The average _____ of an ideal gas is proportional to the _____ temperature. • speed ... Celsius • kinetic energy ... Celsius • speed ... Kelvin • kinetic energy ... Kelvin
Materials • There are four “states” of matter: • Solid • Liquid • Gas • Plasma
Melt or Break?Introduction • Many materials can exist in the solid, liquid, and gaseous states if the forces holding the chemical elements together are strong enough that their melting and vaporization temperatures are lower than their decomposition temperatures. • Hydrogen and oxygen in water, for example, are so tightly bonded that water exists in all three states. • Sugar, on the other hand, decomposes into its constituent parts before it can turn into a gas.
Changes of StateIntroduction • If we continuously heat a solid, the average kinetic energy of its molecules rises and the temperature of the solid increases. • Eventually, the intermolecular bonds break, and the molecules slide over one another (the process called melting) to form a liquid. • The next change of state occurs when the substance turns into a gas. • In the gaseous state, the molecules have enough kinetic energy to be essentially independent of each other. • In a plasma, individual atoms are literally ripped apart into charged ions and electrons, and the subsequent electrical interactions drastically change the resulting substance’s behavior.
Density • One characteristic property of matter is its density. Unlike mass and volume, which vary from one object to another, density is an inherent property of the material. • A ton of copper and a copper coin have drastically different masses and volumes but identical densities. • If you were to find an unknown material and could be assured that it was pure, you could go a long way toward identifying it by measuring its density. • Density is defined as the amount of mass in a standard unit of volume and is expressed in units of kilograms per cubic meter (kg/m3):
Density • For example, an aluminum ingot is 3 meters long, 1 meter wide, and 0.3 meter thick. If it has a mass of 2430 kg, what is the density of aluminum? • We calculate the volume first and then the density: • Densities are often expressed in grams per cubic centimeter. Thus, the density of aluminum is also 2.7 grams per cubic centimeter (g/cm3). Table (next slide) gives the densities of a number of common materials.
Which has the greater density, 1 kilogram of iron or 2 kilograms of iron? • 1 Kg of Iron • 2 Kg of Iron • Both the same • More information is needed.
Conceptual QuestionDensity • Which has the greater density, 1 kilogram of iron or 2 kilograms of iron? Answer: They have the same density. • The density of a material does not depend on the amount of material. ?
Density • The densities of materials range from the small for a gas under normal conditions to the large for the element osmium. • One cubic meter of osmium has a mass of 22,480 kilograms (a weight of nearly 50,000 pounds), about 22 times as large as the same volume of water. • It is interesting to note that the osmium atom is less massive than a gold atom. Therefore, the higher density of osmium indicates that the osmium atoms must be packed closer together.
Density • The materials that we commonly encounter have densities around the density of water, 1 g/cm3. • A cubic centimeter is about the volume of a sugar cube. • The densities of surface materials on Earth average approximately 2.5 g/cm3. • The density at Earth’s core is about 9 grams per cubic centimeter, making Earth’s average density about 5.5 g/cm3.
CrystalsSolids • Crystals grow in a variety of shapes. Their common property is the orderliness of their atomic arrangements. The orderliness consists of a basic arrangement of atoms that repeats throughout the crystal, analogous to the repeating geometric patterns in some wallpapers. • The microscopic order of the atoms is not always obvious in macroscopic samples. • For one thing there are very few perfect crystals; most samples are aggregates of small crystals. However, macroscopic evidence of this underlying structure does exist. A common example in northern climates is a snowflake. Its sixfold symmetry is evidence of the structure of ice.
CrystalsSolids • In contrast to mica, ordinary table salt exhibits a three-dimensional structure of sodium and chlorine atoms. If you dissolve salt in water and let the water slowly evaporate, the salt crystals that form have very obvious cubic structures. • If you try to cut a small piece of salt with a razor blade, you find that it doesn’t separate into sheets like mica but fractures along planes parallel to its faces. • Salt from a saltshaker displays this same structure, but the grains are usually much smaller. A simple magnifying glass allows you to see the cubic structure. • Precious stones also have planes in their crystalline structure. A gem cutter studies the raw gemstones very carefully before making the cleavages that produce a fine piece of jewelry.
CrystalsSolids • Some substances have more than one crystalline structure. A common example is pure carbon. Carbon can form diamond or graphite crystals (Figure 12-3). • Diamond is a very hard substance that is treasured for its optical brilliance. Diamond has a three-dimensional structure. • Graphite, on the other hand, has a two-dimensional structure like mica, creating sheets of material that are relatively free to move over each other. Because of its slippery nature, graphite is used as a lubricant and as the “lead” in pencils.
Liquids • When a solid melts, interatomic bonds break, allowing the atoms or molecules to slide over each other, producing a liquid. • Liquids fill the shape of the container that holds them, much like the random stacking of a bunch of marbles. • The temperature at which a solid melts varies from material to material simply because the bonding forces are different. • Hydrogen is so loosely bound that it becomes a liquid at 14 K. • Oxygen and nitrogen—the constituents of the air we breathe—melt at 55 K and 63 K, respectively. • The fact that ice doesn’t melt until 273 K (0°C) tells us that the bonds between the molecules are relatively strong.
WaterLiquids • Water is an unusual liquid. Although water is abundant, it is one of only a few liquids that occur at ordinary temperatures on Earth. • The bonding between the water molecules is relatively strong, and it requires a high temperature to separate them into the gaseous state.
Surface TensionLiquids • The intermolecular forces in a liquid create a special “skin” on the surface of the liquid. This can be seen in the figure above, in which a glass has been filled with milk beyond its brim. What is keeping the extra liquid from flowing over the edge? • Imagine two molecules, one on the surface of a liquid and one deeper into the liquid. • The molecule beneath the surface experiences attractive forces in all directions because of its neighbors. • The molecule on the surface only feels forces from below and to the sides. • This imbalance tends to pull the surface molecules back into the liquid.
Surface TensionLiquids • Surface tension also tries to pull liquids into shapes with the smallest possible surface areas. • The shapes of soap bubbles are determined by the surface tension trying to minimize the surface area of the film. If there are no external forces, the liquid forms into spherical drops. In fact, letting liquids cool in space has been proposed as a way of making nearly perfect spheres. In the free-fall environment of an orbiting space shuttle, liquid drops are nearly spherical. • Surface tensions vary among liquids. • Water, as you might expect, has a relatively high surface tension. • If we add soap or oil to the water, its surface tension is reduced, meaning that the water molecules are not as attracted to each other. It is probably reasonable to infer that the new molecules in the solution are somehow shielding the water molecules from each other.
Gases • When the molecules separate totally, a liquid turns into a gas. • The gas occupies a volume about 1000 times as large as that of the liquid. • In the gaseous state, the molecules have enough kinetic energy to be essentially independent of each other. • A gas fills the container holding it, taking its shape and volume. • Because gases are mostly empty space, they are compressible and can be readily mixed with each other.
ViscosityGases • Gases and liquids have some common properties because they are both “fluids.” All fluids are able to flow, some more easily than others. • The viscosity of a fluid is a measure of the internal friction within the fluid. • You can get a qualitative feeling for the viscosity of a fluid by pouring it. • Those fluids that pour easily, such as water and gasoline, have low viscosities. • Those that pour very slowly, such as molasses, honey, and egg whites, have high viscosities. • Glass is a fluid with an extremely high viscosity. • In the winter, drivers put lower-viscosity oils in their cars so that the oils will flow better on cold mornings. • The viscosity of a fluid determines its resistance to objects moving through it. A parachutist’s safe descent is due to the viscosity of air. • Air and water have drastically different viscosities. Imagine running a 100-meter dash in water 1 meter deep!
Plasmas • At around 4500°C, all solids have melted. At 6000°C, all liquids have been turned into gases. And at somewhere above 100,000°C, most matter is ionized into the plasma state. • In the transition between a gas and a plasma, the atoms themselves break apart into electrically charged particles. • Although more rare on Earth than the solid, liquid, and gaseous states, the fourth state of matter, plasma, is actually the most common state of matter in the Universe (more than 99%). • Examples of naturally occurring plasmas on Earth include fluorescent lights and neon-type signs. • Fluorescent lights consist of a plasma created by a high voltage that strips mercury vapor of some of its electrons. “Neon” signs employ the same mechanism but use a variety of gases to create the different colors.
Plasma Hubble Telescope Image
ExamplesPlasmas • Perhaps the most beautiful naturally occurring plasma effect is the aurora borealis, or northern lights. • Charged particles emitted by the Sun and other stars are trapped in Earth’s upper atmosphere to form a plasma known as the Van Allen radiation belts. These plasma particles can interact with atoms of nitrogen and oxygen over both magnetic poles, causing them to emit light as discussed in Chapter 23. • Plasmas are important in nuclear power as well as in the interiors of stars.
Pressure • A macroscopic property of a fluid—either a gas or a liquid—is its change in pressure with depth. • Pressure is the force per unit area exerted on a surface, measured in units of newtons per square meter (N/m2), a unit known as a pascal (Pa). • When a gas or liquid is under the influence of gravity, the weight of the material above a certain point exerts a force downward, creating the pressure at that point. Therefore, the pressure in a fluid varies with depth. You have probably felt this while swimming. • As you go deeper, the pressure on your eardrums increases. • If you swim horizontally at this depth, you notice that the pressure doesn’t change. In fact, there is no change if you rotate your head; the pressure at a given depth in a fluid is the same in all directions.
Pressure • Consider the box of fluid shown on the right. • Because the fluid in the box does not move, the net force on the fluid must be zero. • Therefore, the fluid below the box must be exerting an upward force on the bottom of the box that is equal to the weight of the fluid in the box plus the force of the atmosphere on the top of the box. The pressure at the bottom of the box is just this force per unit area. • Our atmosphere is held in a rather strange container, Earth’s two-dimensional surface. Gravity holds the atmosphere down so that it doesn’t escape. • There is no definite top to our atmosphere; it just gets thinner and thinner the higher you go above Earth’s surface.
Atmospheric PressurePressure • The air pressure at Earth’s surface is due to the weight of the column of air above the surface. • At sea level the average atmospheric pressure is about 101 kilopascals. • This means that a column of air that is 1 square meter in cross section and reaches to the top of the atmosphere weighs 101,000 newtons and has a mass of 10 metric tons. • A similar column of air 1 square inch in cross section weighs 14.7 pounds; therefore, atmospheric pressure is also 14.7 pounds per square inch.
Atmospheric PressurePressure • We can use these ideas to describe what happens to atmospheric pressure as we go higher and higher. • You might think that the pressure drops to one-half the surface value halfway to the “top” of the atmosphere. However, this is not true, because the air near Earth’s surface is much denser than that near the top of the atmosphere. This means that there is much less air in the top half compared with the bottom half. • Because the pressure at a given altitude depends on the weight of the air above that altitude, the pressure changes more quickly near the surface. • In fact, the pressure drops to half at about 5500 meters (18,000 feet) and then drops by half again in the next 5500 meters. This means that commercial airplanes flying at a typical altitude of 36,000 feet experience pressures that are only one-fourth those at the surface.
Pressure • As you dive deeper in water, the pressure increases for the same reasons as in air. • Because atmospheric pressure can support a column of water 10 meters high, we have a way of equating the two pressures. • The pressure in water must increase by the equivalent of 1 atmosphere (atm) for each 10 meters of depth. • Therefore, at a depth of 10 meters, you would experience a pressure of 2 atmospheres, 1 from the air and 1 from the water. • The pressures are so large at great depths that very strong vessels must be used to prevent the occupants from being crushed.
Sink and Float • Floating is so commonplace to anyone who has gone swimming that it might not have occurred to ask, “Why do things sink or float?” “Why does a golf ball sink and an ocean liner float?” “And how is a hot-air balloon similar to an ocean liner?” • Anything that floats must have an upward force counteracting the force of gravity, because we know from Newton’s first law of motion (Chapter 3) that an object at rest has no unbalanced forces acting on it. • To understand why things float therefore requires that we find the upward buoyant force opposing the gravitational force.
Sink and Float • The buoyant force exists because the pressure in the fluid varies with depth. • To understand this, consider the cubic meter of fluid in Figure 12-10. The pressure on the bottom surface is greater than on the top surface, resulting in a net upward force. • The downward force on the top surface is due to the weight of the fluid above the cube. • The upward force on the bottom surface is equal to the weight of the column of fluid above the bottom of the cube. • The difference between these two forces is just the weight of the fluid in the cube. Therefore, the net upward force must be equal to the weight of the fluid in the cube.