EPS 5 Framework 0. Physics Basics: The fundamentals --the driest-- 1. Atmospheric Radiation: Energy Balance & Climate 2-3. Atmospheric Physics and Physical Climate Biogeochemical Cycles and Biosphere-Climate Interactions Stratospheric Chemistry Tropospheric Chemistry Bringing it all together: Synthesis

U-tubes: water-air; water paint thinner Collapsing Drum Demonstrations Meter Stick Basketball Spring Scales Ball on a String Golf-Ball Atmosphere U-tubes: water-air; water paint thinner Collapsing Drum clickers: how hard to pull to get 120 deg. angle of spring scales; paint thinner; why doesn't the desk collapse (atm press)

What causes the patterns of wind and pressure? (What is pressure?) January July What causes the patterns of wind and pressure? (What is pressure?) Preface: we start at the beginning, slow and dry—1-2 lectures, hang in there! Motivation: pressure differences in the atmosphere=>drive atmospheric motions (weather, climate) BD: 1. what is pressure? 2. How are pressure gradients produced in the atmosphere? 3. how are winds genreated? 4. Why are atmospheric motions nearly parallel to pressure gradients, instead of perpendicular? 5. Why do winds and pressures form distinctive patterns (climate!)? Materials for this lecture: 1 m stick; 1 balance; 2 1-kg wts; 2 500-g wts; 1 ball-on-a-string; 1 basketball; 3 spring balances; collapsing drum U-tubes, stopcocks at the low point. (a) one side filled with water, one side with air. (b) One side with water, one with paint thinner. Pressure anomaly scale (mb)

Structure of Lecture 2, EPS 5: Define the basic quantities of physics that will be used in the course. Discuss the origin of "units" (needed to make quantitative measurements). Introduce derived quantities and distinguish between scalar quantities (not intrinsically directional) and vector quantities (directional). Focus attention on force, and then on pressure, because of the central role of these quantities in atmospheric processes. Examine the magnitude of the pressure exerted by the atmosphere. Introduce pressure as a phenomenon associated with molecules of a fluid (gas or liquid) hitting a solid object. The relationship between pressure as the weight of overlying fluid and as the force exerted by molecular collisions will lead us, in a later lecture, to understanding why atmospheric pressure decreases with altitude, and will start us towards understanding winds and storms. 27 January 2010

Fundamental quantities of physics MKS cgs () Time s s 1 Length m cm 100 Mass kg g 1000 MKS units = "SI" (standard international units) Once we have defined units (standard measures) for these quantities we can derive for all other quantities of physics. Start with the climate slides (vg?)—for context. We will use *only* SI units. No feet, pounds, Fahrenheit, Discuss the concept of standards very carefully and slowly. Relate the standard measures to everyday life. Discuss unit conversions with an example on the blackboard. Do the following on the board: kg -> g; ng m-> cm ; m->km; m3 -> cm3; m3 ->liters

How are standards for fundamental quantities defined? A standard meter (m) was defined by a metal rod in a vault in Paris. It was supposed to be designed so that 1 m was 1/40,000,000 of the polar circumference. It is now defined by a certain number of wavelengths of laser light from a particular laser. The definitions were required to be such that anyone, anywhere, could set up a way to insure that his/her measurements were equivalent to measurements made by someone in the vault in Paris. The laser is obviously easier to replicate than the piece of metal in Paris, and the light won't change in the future whereas the bar could be destroyed. Initially a standard mass (kg) was a block of metal in Paris, selected so that 1 m3 of water had a mass of about 1000 kg (a metric ton). The standard time (s) was an average day divided by 86400 (24 hours, 3600 seconds in each hour). Largely skip this. Discuss the standards in Paris, why they were developed, why they were superceded. [ ] 1 degree of latitude = 60 nautical miles  100 km (actual value: 60 nm = 111.12 km )

DEMONSTRATION: platform balance. also spring scale DEMONSTRATION: platform balance. also spring scale. Explain why mass is an intrinsic property of an object but weight is not (depends on where you are—gravity etc ) space shuttle, moon, earth comparison. Once the standards are defined, the quantity in any object (mass, dimension) or time span can be determined using devices that compare the object to the standard.

Structure of Lecture 2, EPS 5: Define the basic quantities of physics that will be used in the course. Discuss the origin of "units" (needed to make quantitative measurements. Introduce derived quantities and distinguish between scalar quantities (not intrinsically directional) and vector quantities (directional). Focus attention on force, and then on pressure, because of the central role of these quantities in atmospheric processes. Examine the magnitude of the pressure exerted by the atmosphere. Introduce pressure as a phenomenon associated with molecules of a fluid (gas or liquid) hitting a solid object. The relationship between pressure as the weight of overlying fluid and as the force exerted by molecular collisions will lead us, in the next lecture, to understanding why atmospheric pressure decreases with altitude, and will start us towards understanding winds and storms.

Derived quantities: important combinations of fundamental quantities Quantity, definition Formula Dimensions (units) velocity = distance time L/t m s - 1 acceleration change of velocity v/t 2 force =mass ´ F=m a kg ms º Newtons (N) weight= mass accelera tion of gravity = force exerted by gravity on an object F=mg (same as force; g=9.8 ms ) work = force E=F L kg m s Joules (J) kinetic energy = energy of motion E= mv (same as work) Temperature (related v ia Boltzmann's constant, k, to the mean kinetic energy of a gas molecule) = kT [non dimensional, units=degrees Kelvin; k=1.38 10 23 J/K] pressure force per unit area P = F/A Board—write down Newton’s law, F=ma on the board. E=F L. Show how the units work Note that 1 kg =>> 9.8 Newtons on earth NOTE that LENGTH (displacement) is a vector—it matters which way you move! velocity is also a vector, and acceleration and force too. discuss each concept as things we experience. likewise energy – both kinetic and work. mini-demo: toss the ball; consider its velocity, acceleration (by my toss and by gravity), its energy; NB the force that it exerts when it hits something. real demo– illustrate force is a vector with 2 spring scales; show how a force balance results from opposed forces. => the object does not move. we need the table of factors here. Add nautical miles  km and radius of the earth. knot  m/s The relationships between fundamental and derived quantities are intimately tied to the laws of physics. For example, Newton's laws relate familiar quantities (force, energy) to the fundamental quantities. vectors

Some physical quantities are vector quantities Some physical quantities are vector quantities. In order to use these quantities in studying a physical phenomenon, both the magnitude and the direction must be specified. If equal forces act on an object in opposite directions, it will not start to move (a = 0 ). If equal forces act on an object in same direction, it will start to move (a  0 ). Vector quantities include length, velocity, acceleration, force, and pressure. Quantities that do not have an associated direction ("scalar" quantities) include energy, mass, and time. In EPS-5 we need to understand the concept of a vector but we will not do "vector algebra" involving adding, multiplying, etc. Demo with spring scales—first 1, accelerate a weight; then 2 in balance, then three --first me, then students. students ("you can do vector algebra")—three spring scales. Have the students do this. two pull. then a third one. How is a balance achieved? “zero net force” -- and what do we mean by a net force? Newton’s 2nd law, acceleration. The net effect of all the forces—obviously two people pulling at the given angle(s) are exactly equivalent to one pulling opposite to the third, with the same force as the third! Vector algebra– right angles, 10/7/7 next demo—twirl the ball on the string. Discuss the acceleration. What is going on?

A related quantity is the "number of atoms of an element that have mass equal to the elemental mass in grams", Avogadro's number: N0 = 6.02  1023 In the 18th centrury, the concepts of mass and density (mass/vol) were known, but atoms were not. However knowledge of atoms came rather early, and by the 19th century chemists has determined the relative amount of mass needed to make a chemical compound from its components—for example, 12 g of carbon + 32 g of Oxygen to make a gas now known to be CO2. Atomic or molecular weights were defined, with H as 1 (approximately) and carbon as 12 (exactly). Then the “indivisible” mass was determined, and the number of atoms in a “mole” (number needed to make up the atomic or molecular mass) was determined- Avogadro’s number. 6.02 x 1023. It is a derived quantity. mass of 1 mole of an element in grams = "molecular weight" =mass of N0 atoms a convenient number relating the molecular and macroscopic scales

Density = mass/unit volume = r = M/V (kg/m3). Pressure is a particularly important concept for studying the atmosphere. It is related to force and weight. Force and Weight The weight of an object is the force caused by the gravitational acceleration (g) acting on the object, which is proportional to its mass (m), weight = mg. g = acceleration of gravity = 9.8 m/s/s. The distance a spring extends with a given weight on it depends on the acceleration of gravity acting on the object attached to the spring. If we take the spring to the moon, where the gravitational acceleration is much small than on the earth, the object will weigh less, even though its mass has not changed. As a result, the spring will not extend as much as it did on the earth. Weight is not an intrinsic property of an object. Mass is the intrinsic property. Density = mass/unit volume = r = M/V (kg/m3). Density is an intrinsic property specific to a particular material (air, brass, steel, etc) at a given temperature and pressure. It is an intensive quantity as opposed to mass being an extensive property. Calculate the mass and weight of 1 m3 of water--clicker. Define density = mass/volume. Note this is a property of a material (air, steel) intensive property, whereas mass is a property of an object extensive property [increases if you have two objects…] bd: intensive = property of a material extensive = property of an object

Pressure Pressure means the force (F), or weight, of an object distributed over a surface area (A) equal to 1 meter (Force per unit area). (The acceleration of gravity is 9.8 m s-2, and the force F = mg). We often refer to the pressure of the earth's atmosphere at the surface as 1 atmosphere (atm). A container of water 10 m high, by 1 m wide, by 1 m deep holds 10 cubic meters of water, or 10,000 kg of mass. Thus the pressure of the water on the bottom of this container would also be about 1 atm. This means that an individual swimming 10 m underwater would feel a pressure of 2 atm (1 atm from the weight of the atmosphere and 1 atm from the weight of the water) on his/her body. Draw the container on the board. Do a stepwise calculation: BD: Pressure = Force/area = wt/area Find Wt/area. Little box diagram with 1 m2 xsect.  = kg/m3  g = Newtons/m3  gh = Newtons/m2 P = gh; do this slowly: volume of box = 10 m3; 1000 kg/m3 => 104 kg weight= 9.8x104; P=105 N/m2 10m 1m2

Structure of Lecture 2,EPS 5: Define the basic quantities of physics that will be used in the course. Discuss the origin of "units" (needed to make quantitative measurements. Introduce derived quantities and distinguish between scalar quantities (not intrinsically directional) and vector quantities (directional). Focus attention on force, and then on pressure, because of the central role of these quantities in atmospheric processes. Examine the magnitude of the pressure exerted by the atmosphere. Introduce pressure as a phenomenon associated with molecules of a fluid (gas or liquid) hitting a solid object. The relationship between pressure as the weight of overlying fluid and as the force exerted by molecular collisions will lead us, in the next lecture, to understanding why atmospheric pressure decreases with altitude, and will start us towards understanding winds and storms.

Why doesn't the desk collapse? The weight of the atmosphere exerts a pressure on the surface of the earth. This pressure is 100,000 Newtons (N)/sq meter, corresponding to a mass m of slightly more than 10,000 kg of air over every square meter of the earth's surface. A city bus might weigh about 10,000 kg, and your desk might have an area of roughly 1 m2. Thus the weight of the atmosphere on your desk is about 10 metric tons. Why doesn't the desk collapse? Since the air is not moving (falling), there must be an upward force that balances its weight. What is that? Since the atmosphere is not falling down, there must be an upward force that balances its weight. What is that?

Perfect gas law (a.k.a. Boyle's and Charles' Laws) PV = NkT To answer this we have to understand how a gas (the atmosphere) exerts pressure on a surface. Suppose we have air molecules in a container. The molecules in the gas are moving all the time. When they hit a solid surface, they bounce off. This change in direction of motion is a change in the velocity, equivalent to an acceleration and hence a force is exerted on the surface. The force depends on the mass and velocity (temperature) of each molecule, and on the number of molecules. (The “golf ball atmosphere" demonstration in class illustrates this effect.) Experiments carried out in the 19th century showed that there is a very simple formula that expresses the relationship between the temperature, pressure, and number of molecules in a volume: Perfect gas law (a.k.a. Boyle's and Charles' Laws) PV = NkT where P is pressure, V volume, N the number of molecules in the volume, and T the absolute temperature (Kelvin; T(K)=T(C)+273.15); k is Boltzmann's constant (1.38 x 10-23 Joules/Kelvin). N = number of molecules in the volume V Use the basketball , then ping-ping atmosphere. Focus on Boyle’s law ( P1V1 = P2 V2 ) [T fixed] and Charles’ Law P1/T1 = P2/T2 [V fixed]. Note T is in Kelvin’s!!! Note we don’t do Fahrenheit’s.

n = number of molecules m -3 The Perfect Gas Law relates pressure to temperature (the kinetic energy of the molecules) and "number density". Since we don't have confined volumes in the atmosphere, we usually use this very important relationship in the form, P = nkT, where n (= N/V, the number density) is the number of molecules per unit volume. A relationship to remember. Emphasis on what this means—changes in P; n; T. n = number of molecules m -3

Pressure in a fluid--can cause the fluid to move Pressure in a fluid--can cause the fluid to move! In both tanks the atmosphere exerts a pressure of 1 atm on the surface of the water (blue) in each tank, and the weight of the water provides additional pressure, so the pressure on the bottom is the sum of atmospheric and water pressure. The picture on the left side illustrates that, since pressure is a measure of force per unit area, it doesn't matter how wide the the arm of the tank is! It only matters how much fluid is resting above a unit area of the bottom of the tank. Therefore, in the experiment on the left, where the height of the fluid in the two tanks is the same, the pressures at the bottom of the tanks are equal, forces are balanced, and the fluid does not move. water air fluid will start to move

On the other hand, in the experiment on the right, the side of the tank which has a higher column of fluid will exert a greater force on the bottom than the side with the lower column of fluid. This is not a stable situation. We would expect the fluid to flow from high pressure to low pressure (from the tank on the left to the tank on the right) until the pressures are equal - when the height of the fluid in the two tanks are the same. water air fluid will start to move

Structure of Lecture 2, EPS 5: Define the basic quantities of physics that will be used in the course. Discuss the origin of "units" (needed to make quantitative measurements. Focus attention on force, and then on pressure, because of the central role of these quantities in atmospheric processes. Examine the magnitude of the pressure exerted by the atmosphere. Introduce derived quantities and distinguish between scalar quantities (not intrinsically directional) and vector quantities (directional). Introduce pressure as a phenomenon associated with molecules of a fluid (gas or liquid) hitting a solid object. The relationship between pressure as the weight of overlying fluid and as the force exerted by molecular collisions will lead us, in the next lecture, to understanding why atmospheric pressure decreases with altitude, and will start us towards understanding winds and storms. 27 January 2010