seasonal changes in temperature, pressure, winds: even...

January July

Pressure anomaly scale (mb)

Seasonal changes in temperature, pressure, winds: even though weather is very variable and climate changes appear small in comparison, climate is critically important in

shaping life on earth.

Structure of Lecture 2, Science A-30:

1. Define the basic quantities of physics that will be used in the course.

2. Discuss the origin of "units" (needed to make quantitative measurements).

3. Introduce derived quantities and distinguish between scalar quantities (not intrinsically directional) and vector quantities (directional).

4. Focus attention on force, and then on pressure, because of the central role of these quantities in atmospheric processes.

5. Examine the magnitude of the pressure exerted by the atmosphere.

6. 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.

05 February 2008

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.

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 100 km (105 m) was 1 degree of latitude. 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).

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.



2. Discuss the origin of "units" (needed to make quantitative measurements.






Derived quantities: important combinations of fundamental quantities

The relationships between fundamental and derived quantities areintimately tied to the laws of physics. For example, Newton's laws relate familiar quantities (force, energy) to the fundamental quantities. vectors

Quantity, definition Formula Dimensions (units)

velocity= distance

time L/t m s-1

acceleration = change of velocity

time v/t m s-2

force=mass×acceleration F=m a kg ms-2 ≡ Newtons (N)weight= mass×acceleration of gravity

= force exerted by gravity on an object

F=mg (same as force; g=9.8 ms -2)

work = force×distance E=F• L kg m2 s-2 ≡ Joules (J)

kinetic energy = energy of motion E=12 mv2 (same as work)

Temperature (related via Boltzmann's constant, k, to the mean kinetic energyof a gas molecule)

12 mv2 = kT

[non-dimensional, units=degrees Kelvin; k=1.38 10-23 J/K]

pressure = force per unit area P = F/A kg m-1 s-2

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 Sci-A30 we need to understand the concept of a vector but we will not do "vector algebra" involving adding, multiplying, etc.

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

Pressure is a particularly important concept for studying the atmosphere. It is related to force and weight.Force and WeightThe 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 = ρ = 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 anintensive quantity as opposed to mass being an extensive property.

Pressure

Pressure means the force (F), or weight, of an object distributed over asurface 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 atmfrom the weight of the water) on his/her body.

1m2

10m

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 atmosphere is not falling down, there must be an upward force that balances its weight. What is that?

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.

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

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.

The Perfect Gas Law relates pressure to temperature (the kinetic energy of the molecules) and "number density".

n = number of molecules m -3

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.

waterair

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.

waterair

fluid will start to move









05 February 2008

seasonal changes in temperature, pressure, winds: even...

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