Chapter 4Physics of Matter

Matter: Phases, Forms & ForcesWe classify matter into four categories:Solid: rigid; retain its shape unless distorted by a force.Liquid: flows readily; conforms to the shape of a container; has a well-defined boundary; has higher densities than gases.Gas: flows readily; conforms to the shape of a container; does not have a well-defined surface; can be compressed readily.Plasma: has gaseous properties but also conducts electricity; interacts strongly with magnetic fields; commonly exists at higher temperatures.

Matter: Phases, Forms & Forces, contdThe chemical elements represent the simplest and purest forms of everyday matter.There are currently 114 different elements.110 of them have accepted names.Each element is composed of incredibly small objects called atoms.There are 114 different atoms, one for each of the known elements.Only about 90% of the elements exist naturally on Earth.The others are artificially produced in laboratories.

Matter: Phases, Forms & Forces, contdThe atom is not indivisible.It has its own internal structure.Every atoms has a very dense, compact core called the nucleus.The nucleus is composed of two kinds of particles:Protons: have a positive electric charge.Neutrons: have no electric charge.The nucleus is surrounded by one or more particles called electrons.Electrons have the same electric charge as protons but are negatively charged.

Matter: Phases, Forms & Forces, contdEvery atom associated with a particular element has a fixed number of protons.The number of protons distinguishes the element.Atoms with two protons are helium atoms.The atomic number of an element specifies the number of protons.The atomic number of helium (He) is 2 because it has two protons.Each element is given its own chemical symbol.This is a one- or two- letter abbreviation.

Matter: Phases, Forms & Forces, contdAtoms can have various numbers of neutrons.Atoms with different numbers of neutrons for a certain elements are called isotopes.More on this in chapter 11.

Matter: Phases, Forms & Forces, contdChemical compounds are the next simplest form of everyday matter.Examples: water, salt, sugar, etc.Compounds are made from building blocks called molecules.Every molecule of a particular compound consists of the same unique combination of two or more atoms.Each water molecule consists of two hydrogen atoms and one oxygen atom.

Matter: Phases, Forms & Forces, contdEach compound can be represented by a chemical formula.water is H2O;salt is NaCl;carbon dioxide is CO2;sugar is C12H22O11;ethyl alcohol is C2H5OH.

Matter: Phases, Forms & Forces, contdMany substances are composed of two or more different compounds that are physically mixed together called mixtures and solutions.Air is a mixture of several gases.The actual composition varies widely from day to day and place to place.

Behavior of atoms and moleculesThe constituent particles of atoms and molecules exert electrical forces on each other.Static cling is an example of an electrical force.The forces depend upon the configuration of the atoms in each atom.

Behavior of atoms and molecules, contdSolids: Attractive forces between particles are very strong; the atoms or molecules are rigidly bound to their neighbors and can only vibrate.Liquids: The particles are bound together, though not rigidly; each atom or molecules move about relative to the others but is always in contact with other atoms or molecules.Gases: Attractive forces between particles are too weak to bind them together; atoms or molecules move freely with high speed and are widely separated; particles are in contact only when they collide.

Behavior of atoms and molecules, contdAtoms or molecules in a solid arranged in a regular geometric pattern are called crystals.Solids that do not have a regular crystal structure are called amorphous solids.

Behavior of atoms and molecules, contdCarbon has two common crystalline forms.Graphite forms crystalline sheets with little bonding between sheets.Diamond forms very strong bonds between adjacent carbons its the hardest known natural substance.

Behavior of atoms and molecules, contdIn liquids, the inter-atomic forces are insufficient to bind the atoms rigidly.The atoms are free to move and vibrate.In gases, the inter-atomic forces are virtually negligible unless the atoms are very close.Gaseous atoms have rather high speeds: ~1,000 mph.

Behavior of atoms and molecules, contdWhenever a high-speed gas atom impacts a large force on a container.It is this force that produces a pressure on the container.As the air molecules strike the inside of a tire, they produce the pressure that inflates the tire.If the molecules are stationary, there is no pressure.

Behavior of atoms and molecules, contdGases are easily compressed because the majority of their volume is the space between the atoms.If you compress it enough, you force the atoms close enough together that you form a liquid.

PressurePressure is the force per unit area for a force acting perpendicular to a surface.Since we use the perpendicular component of the force, pressure is a scalar.

Pressure, contdThe units of pressure are:Metric:pascal (Pa; 1 Pa = 1 N/m2) SI unit;millimeters of mercury (mm Hg).English:pound per square foot (lb/ft2);pound per square inch (lb/in2 or psi);inches of mercury (in. Hg).

Pressure, contdSome pressure conversions:1 psi = 6,890 Pa.We also use an atmosphere (atm) as a pressure unit:One atmosphere is the average pressure exerted by air at sea level:1 atm = 1.01105 Pa;1 atm = 14.7 psi.

Pressure, contd

ExampleExample 4.1A 160-pound person stands on the floor. The area of each show that is in contact with the floor is 20 square inches. What is the pressure on the floor? Assume the persons weight is shared equally between the two shows.

ExampleExample 4.1ANSWER:The problem gives us:

Since the shoes support the weight equally, each show must support a weight of 80 lb.The pressure is

ExampleExample 4.1DISCUSSION:If the person stands on only one foot:

If the person wore high heels and stood on only one heel (0.5 in by 0.5 in):

ExampleExample 4.2In the late 1980s, there were several spectacular aircraft mishaps involving rapid loss of air pressure in the passenger cabins.The cabin pressure of a passenger jet cruising at high altitude (25,000 ft) is about 6 psi (0.41 atm) greater than the pressure outside. What is the outward force on a window measuring 1 foot by 1 foot and on a door measuring 1 meter by 2 meters?

ExampleExample 4.2ANSWER:The force on the window is:

The force on the door is

ExampleExample 4.2DISCUSSION:The force on a window is approximately the weight of four adults.

The force on the door is nearly the weight of five pickups.

Pressure, contdPressure is a relative quantity.When you measure a pressure, you are measuring it relative to some other pressure.When you measure your tire pressure, you are measuring the pressure in the tire above the atmospheric pressure.

Pressure, contdThe gauge pressure is the pressure relative to the current atmospheric pressure.The absolute pressure is the gauge pressure plus the atmospheric pressure.

Pressure, contdThe standard pen-shaped tire gauge compares the tire pressure against a spring and the atmospheric pressure.

Pressure, contdAn important statement about gases.Consider a gas held at constant temperature.Increasing the temperature increases the motion of the gas atoms and therefore the pressure.Under these conditions:

Pressure, contdThis means:Decreasing the volume increases the pressure.Imagine squeezing part of an inflated balloon.Decreasing the pressure increases the volume.Imagine letting the air out of an inflated balloon.

DensityMass density is the mass per unit volume of a substance.It is the ratio of the mass to the volume of the substance.

Density, contdUnits of mass density:Metric:kilogram per cubic meter (kg/m3);gram per cubic centimeter (g/cm3).English:slug per cubic foot (slug/ft3).

Density, contdMeasure density by finding the mass of a sample and dividing by the volume of the sample.The actual size of the sample is irrelevant.If you use a sample with twice the volume you will twice the mass.

Density, contdYou can measure the freezing point of your cars coolant by measuring the density.The density of water and antifreeze are different.Water: 1,000 kg/m3.Antifreeze: 1,100 kg/m3.The overall density depends on the ratio of the amount of water and amount of antifreeze.

ExampleExample 4.3The dimensions of a rectangular aquarium are 0.5 meters by 1 meter by 0.5 meters. The mass of the aquarium is 250 kilograms larger when it is full of water than when it is empty. What is the density of the water?

ExampleExample 4.3ANSWER:The problem gives us:

The volume is:

ExampleExample 4.3ANSWER:The mass density is then

ExampleExample 4.3DISCUSSION:If the width of the tank was doubled, the amount of water would be doubled the density would remain the same.If filled with gasoline, the mass is 170 kg. The density of gasoline is

Density, contdIf you know the volume and what type of substance you have, you can find the mass:

ExampleExample 4.4The mass of water needed to fill a swimming pool can be computed by measuring the volume of the pool. Lets say a pool is going to be guilt that will be 10 meters wide, 20 meters long, and 3 meters deep. How much water will it hold?

ExampleExample 4.4ANSWER:The problem gives us:

The volume is:

ExampleExample 4.4ANSWER:Since the density of water is 1,000 kg/m3, the amount of water is:

ExampleExample 4.4DISCUSSION:Since a common bathtub is about 0.25 m3 (lets say 1 m by 0.5 m by 0.5 m), this swimming pool is about 2400 bathtubs of water.

Density, contdWeight density is the weight per unit volume of a substance.It is the ratio of the objects weight and its volume.

Density, contdUnits or weight density:Metric:newton per cubic meter (N/m3).English:pound per cubic foot (lb/ft3);pound per cubic inch (lb/in3).

ExampleExample 4.5A college dormitory room measures 12 feet wide by 16 feet long by 8 feet high. What is the weight of the air in it under normal conditions?

ExampleExample 4.5ANSWER:The problem gives us:

The volume is:

ExampleExample 4.5ANSWER:The weight of the air in the room is

ExampleExample 4.5DISCUSSION:Notice that as the temperature increases, the density would decrease.So the air in the room would weigh less on hotter days.Because there is less air (fewer air molecules) in the room.

Fluid pressure and gravityThe law of fluid pressure states that the (gauge) pressure at any depth in a fluid at rest equals the weight of the fluid in a column extending from that depth to the top of the fluid divided by the cross-sectional area of the column.

Fluid pressure and gravity, contdMathematically,

The force is:

The area is:

Fluid pressure and gravity, contdWe can write then write the pressure as:

The pressure depends on:the fluids density,the gravitational acceleration, andthe depth of the fluid

Fluid pressure and gravity, contdNote that this is the gauge pressure at the depth h.To get the absolute pressure, we need to add the atmospheric pressure pushing down at the top of the fluid column.

ExampleExample 4.6Lets calculate the gauge pressure at the bottom of a typical swimming pool one that is 10 feet (3.05 meters) deep.

ExampleExample 4.6ANSWER:The problem gives us:

The gauge pressure is:

ExampleExample 4.6DISCUSSION:To convert this to psi:

Fluid pressure and gravity, contdThe general result for pressure increase under water is:

The pressure increases 4.33 psi for every 10 ft.It increases by 1 atm every 10 meters, or about 35 feet.

ExampleExample 4.7At what dept in pure water is the gauge pressure 1 atmosphere?

ExampleExample 4.7ANSWER:The problem gives us:The pressure depends on depth according to:

Rearranging for the depth:

ExampleExample 4.7DISCUSSION:If you went swimming in mercury, which is 13.6 times as dense as water:

Fluid pressure and gravity, contdThe atmosphere exerts a pressure on everything since there is a very high column of air above Earths surface.The column height for air, water and mercury are different because the mass densities are increasingly larger.

Fluid pressure and gravity, contdA device to measure air pressure is a barometer.As the air pressure increases, it exerts a larger pressure on the fluids surface.The forces the fluid farther up the tube.The height of the column in the tube indicates the air pressure.

Archimedes principleWeve found that the force of gravity on a fluid causes the pressure to increase with depth.This means that the mass density of the fluid actually decreases with depth.We typically neglect this fact to keep things simple.This produces something we call a buoyant force that exerts an upward force on an object placed in a fluid.

Archimedes principle, contdThe buoyant force is an upward force exerted by a fluid on a substance partly or completely immersed in the fluid.The buoyant force depends on the density of the fluid and the substance.

Archimedes principle, contdArchimedes principle states that the buoyant force acting on an object in a fluid at rest is equal to the weight of the fluid displaced by the object.

This means the object will sink until the weight of the object equals the weight of the water displaced by the object.

Archimedes principle, contdConsider weighing an object in air and then partly immersed in water.In air, the scale must support the entire weight.In water, the buoyant force adds an additional upward force.The scale reads less.

Archimedes principle, contdMathematically, we can write the buoyant force as:

ExampleExample 4.8A contemporary Huckleberry Finn wants to construct a raft by attaching empty, plastic, 1-gallon milk jugs to the bottom of a sheet of plywood. The raft and passengers will have a total weight of 300 pounds. How many jugs are required to keep the raft afloat on water?

ExampleExample 4.8ANSWER:The problem gives us:

The buoyant force is:

Rearranging for the necessary volume:

ExampleExample 4.8ANSWER:The necessary volume to just float is:

ExampleExample 4.8DISCUSSION:So Huck needs at least 36 jugs.Note that he would just float.For a safety margin, you should probably have many more than just 36 jugs just in case a wave rolls through or you want to take a friend along.

Pascals PrinciplePascals Principle states that the pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and to the walls of the container.This principle is used in hydraulic systems.hydraulic lifts, braking systems,etc.

Pascals Principle, contdThe piston on which the force is applied (left) has a small area:

The piston that applies the force (right) has a larger area:

Pascals Principle, contdSince the pressures are the same, the output force is:

With the output pistons area larger than the input pistons area, the output force is larger than the input force.

Pascals Principle, contdA common example is the braking system in your car.

Bernoullis principleSo far we spoke only of static fluids.We now talk about moving fluids.Bernoullis principle states that for a fluid undergoing steady flow, the pressure is lower where the fluid is flowing faster.Steady flow means the fluid flow is smooth.No random swirling, eddies, or white water.

Bernoullis principle, contdOne idea behind the Bernoulli principle is:The amount of mass passing through an area during an amount of time must be the same throughout the pipe.There additional fluid enters or leaves the pipe so what goes in must come out.

Bernoullis principle, contdIn order for the same amount of mass to pass through a cross-section of the wide and narrow sections in a certain amount of time, the fluid must flow faster in the narrow section.

Bernoullis principle, contdThe other idea behind the Bernoulli principle is energy conservation.We can consider the fluid to have a pressure potential energy. The greater the pressure, the greater the PE.

Bernoullis principle, contdJust as with a falling ball, as the PE decreases the KE increases.So as the pressure decreases, the pressure PE decreases.By energy conservation, the KE must increase.

Bernoullis principle, contdAnother example is an atomizer.When you squeeze the bulb, you increase the pressure in the nozzle.This lowers the pressure in the nozzle.The higher pressure in the bottle draws the fluid up the tube.The moving air carries the fluid out of the nozzle.

Heat a coke can with some water to boiling. Turn the can upside-down into a cold bowl of water.Heat a coke can with some water to boiling. Turn the can upside-down into a cold bowl of water.Heat a coke can with some water to boiling. Turn the can upside-down into a cold bowl of water.Heat a coke can with some water to boiling. Turn the can upside-down into a cold bowl of water.Use the pascal syringe with colored water.Use the pascal syringe with colored water.Use the Pascal squitter.Use the pascal syringe with colored water.Use the pascal syringe with colored water.Use the Pascal squitter.Use the pascal syringe with colored water.Use the pascal syringe with colored water.Use the Pascal squitter.Use the pascal syringe with colored water.Use the pascal syringe with colored water.Use the Pascal squitter.Blow across a piece of paper.Blow across a piece of paper.