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ISNS 3371 - Phenomena of Nature The Gas Laws ISNS 3371 - Phenomena of Nature Properties of gases • • • • • • Very compressible. Acquires shape of its container, Completely fills any closed container. Very low density compared with a liquid or a solid. Exhibits a pressure on the walls of its container. Pressure = force per unit area P = F/A Force has direction. Force giving rise to pressure is always perpendicular to the surface. ISNS 3371 - Phenomena of Nature Gas Laws P = pressure of gas V = volume of gas T = absolute (kelvin) temperature of gas – Boyle's Law: – Charles’ Law: – Guy Lussac’s law – General or ideal gas law PV = constant, if T is constant V/T= constant, if P is constant P/T = constant, if V is constant PV/T = constant PV = n RT • R = general gas constant = 8.314 joules/degree-mole • n = number of moles of gas - a mole is 22.4 liters of a gas Ideal gas - one in which we can ignore interactions between the gas molecules. Most gases behave in the same universal way as long as the temperature is kept far from the liquefaction temperature. ISNS 3371 - Phenomena of Nature Guy Lussac’s Law and Absolute Zero Remember third law of thermodynamics: No system can reach absolute zero. How do you determine absolute zero? Consider Guy Lussac’s law: P/T = constant, if V is constant This is for an ideal gas Temperature must get smaller as pressure gets smaller Theoretically, as pressure goes to zero, temperature must go to some smallest value This value is absolute zero and can be determined by measuring the pressure and temperature of a gas at several values and extrapolating to zero pressure ISNS 3371 - Phenomena of Nature Boyle’s Law PV = constant, if T is constant ISNS 3371 - Phenomena of Nature The Law of Adiabatic Expansion (or Compression)) Any gas will cool that is allowed to expand freely from a higher pressure to a lower pressure without the transfer of external energy to the gas. Similarly, a gas will heat if compressed from a lower to a higher pressure in the absence of a transfer of energy from the gas. Consider gas in a bicycle pump: Push the pump in quickly - the gas heats up – you are doing work on the gas. Pull the pump out quickly - gas will cool down - the gas is doing work for you. On a molecular scale. The gas particles are moving with a speed that is determined by the temperature of the gas: Push the pump in - the particles speed up - when they collide with the oncoming piston, they rebound more quickly - they heat up. Pull the pump out - the particles slow down - when they collide with the outgoing piston, they rebound more slowly - they cool down. ISNS 3371 - Phenomena of Nature The same reasoning works for a gas that is expanding freely. Rather than bouncing off a container, the particles bounce off each other. But they are all moving outwards. So any collisions at the edges of the gas will have the effect of taking some of the speed off the expanding molecules. Explains why fog formed in chamber when pressure suddenly reduced: All air contains water vapor of varying quantities. A state of saturation exists when the air is holding the maximum amount of water vapor possible at the existing temperature and pressure. Dew point - the temperature to which the air would have to cool in order to reach saturation - indicates the amount of moisture in the air. Condensation of water vapor begins when the temperature of air is lowered to its dew point and beyond - results in the formation of tiny water droplets that leads to the development of fog, frost, clouds, or even precipitation. When the air in the chamber suddenly expands, the temperature of the air is suddenly reduced to below the dew point and the water vapor condenses to form fog in the chamber. Why is your breath colder when blown out through pursed lips? ISNS 3371 - Phenomena of Nature Bernoulli Effect For horizontal fluid flow, an increase in the velocity of flow will result in a decrease in the static pressure. ISNS 3371 - Phenomena of Nature The Airfoil (Wing) and the Bernoulli Effect The air across the top of the airfoil experiences increased air speed relative to the wing - it must go farther to reach the back edge of the airfoil. This causes a decreases in pressure and provides a lift force. Increasing the angle of attack gives a larger lift from the upward component of pressure on the bottom of the wing. The lift force can be considered to be a Newton's 3rd law reaction force to the force exerted downward on the air by the wing. At too high an angle of attack, turbulent flow increases the drag dramatically and will stall the aircraft. ISNS 3371 - Phenomena of Nature How Does an Airplane Fly Upside Down? If the greater curvature on top of the wing and the Bernoulli effect are evoked to explain lift, how is this possible? An increase in airstream velocity over the top of the wing can be achieved with airfoil surface in the upright or inverted position - requires adjustment of the angle of attack. Typical asymmetric shape of airfoil increases efficiency of lift production but not essential for producing lift. ISNS 3371 - Phenomena of Nature The Curve Ball and the Bernoulli Effect A non-spinning baseball or a stationary baseball in an airstream exhibits symmetric flow. A baseball which is thrown with spin will curve because the air flows faster on one side of the ball than the other side because of friction. So one side of the ball will experience a reduced pressure. The roughness of the ball's surface and the laces on the ball are important! With a perfectly smooth ball you would not get enough interaction with the air. ISNS 3371 - Phenomena of Nature Balancing Ball and the Bernoulli Effect A ball balances on a stream of air because of the Bernoulli effect. If the ball is displaced from the center of the air stream, it will feel a force pulling it back into the center. The air on the right side of the ball in not moving so pressure is lower on the left side of the ball and the ball feels a force toward the center of the air stream. No matter which direction the ball is deflected, it is attracted to the center of the air stream, and stays balanced. ISNS 3371 - Phenomena of Nature Archimedes’ Principle Archimedes Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object. Remember from Pascal’s Law - the difference in pressure between any two places in a single fluid is dependent on tne vertical difference of level of the fluid and at any place in a fluid, pressure pushes equally in all directions. So, the sideways forces on an object are balanced and oppose each other equally, but the upward and downward forces are not the same. The pressure at the bottom of the object is greater than the pressure at the top of the object, because pressure increases with increasing depth. The difference between the upward and downward forces acting on the bottom and the top of the object, respectively, is called buoyancy. ISNS 3371 - Phenomena of Nature Specific Gravity If the mass of an object is less than the mass of an equal volume of water, the bouyant force is greater than the weight of the object and it will float. So the specific gravity is defined as the heaviness of a substance compared to that of water, and it is expressed without units. If something is 7.85 times as heavy as an equal volume of water (such as iron is) its specific gravity is 7.85. Its density (mass per unit volume) is 7.85 grams per cubic centimeter. (The density of water is 1 gr/cm3.) An object with a specific gravity less than 1 will float. A object with specific gravity greater than 1 will sink. Suppose you had equal sized balls of cork, aluminum and lead, with respective specific gravities of 0.2, 2.7, and 11.3 . If the volume of each is 10 cubic centimeters then their masses are 2, 27, and 113 gm. The cork floats and the aluminum and lead sink. ISNS 3371 - Phenomena of Nature A steel rowboat placed on end into the water will sink because the density of steel is much greater than that of water. However, in its normal, keel-down position, the effective volume of the boat includes all the air inside it, so that its average density is then less than that of water, and as a result it will float. Hot air balloons rise into the air because the density of the air (warmer air) inside the balloon is less dense than the air outside the balloon (cooler air). The balloon and the basket displaces a fluid that is heavier than the balloon and the basket, so it has a buoyant force acting on the system. Balloons tend to fly better in the morning, when the surrounding air is cool. ISNS 3371 - Phenomena of Nature Archimedes’ principle is useful for determining the volume and therefore the density of an irregularly shaped object by measuring its mass in air and its effective mass when submerged in water. effective mass under water = actual mass - mass of water displaced (bouyant force) The difference between the real and effective mass therefore gives the mass of water displaced and allows the calculation of the volume of the irregularly shaped object The mass divided by the volume thus determined gives a measure of the average density of the object. Archimedes found that the density of the king's supposedly gold crown (14.2 gr/cm3) was actually much less than the density of gold (19.3 gr/cm3) -implying that it was either hollow or filled with a less dense substance. 440 gr/31cm3 = 14.2 gr/cm3 ISNS 3371 - Phenomena of Nature Waves A wave is a pattern which is revealed by its interaction with particles. It is a vibration - a movement of particles up and down, side-to-side, or back and forth. Waves on a Pond Animation Wave is moving up and down but not outward - carries energy but not matter. Sound and light are both waves - but different. Sound is the movement of vibrations though matter - solids, liquid, or gases - no matter, no sound. Cannot travel in a vacuum. Light is a vibration of electric and magnetic fields - pure energy does not require matter. ISNS 3371 - Phenomena of Nature Properties of Waves Any traveling wave will take the form of a sine wave. The position of an object vibrating in simple harmonic motion will trace out a sine wave as a function of time. (Or if a mass on a spring is carried at constant speed across a room, it will trace out a sine wave.) This transverse wave is typical of that caused by a small pebble dropped into a still pool. Crest - high point of sine wave Crest Trough - low point of sine wave Amplitude (a): maximum displacement from equilibrium Wave length (l): distance between successive crests Trough ISNS 3371 - Phenomena of Nature Properties of Waves Period: time to complete one cycle of vibration - from crest to crest or trough to trough Frequency (f): number of crests passing a fixed point per second Frequency= 1/period Example: Period = 1/100 = 0.01 sec. Frequency = 100 hertz (cycles/sec.) Speed (of a wave) (s)= wave length x frequency s= l x f ISNS 3371 - Phenomena of Nature Anatomy of a Wave Animation ISNS 3371 - Phenomena of Nature Wavelength and Frequency Animation ISNS 3371 - Phenomena of Nature TYPES OF WAVES Transverse: Vibration or oscillation is perpendicular to direction of propagation of wave. Examples: water wave, vibrating string, light Longitudinal: Vibration or oscillation is in the same direction as propagation of wave. Examples: sound waves, mass on a spring, loudspeaker