School Science Lessons
20. Gas laws, ideal gas, Charles' law, Boyle's law, pressure law, density
of gases, thermodynamics, isothermal and adiabatic change
2012-01-24 SP
Please send comments to: J.Elfick@uq.edu.au
Table of contents
20.0.0 Gas laws
20.0.5 Combined gas equation, P1V1
/ T1 = P2V2 / T2
20.1.0 Constant pressure, Charles' law (Gay-Lussac's law)
20.2.0 Constant temperature, Boyle's law (Mariotte's law)
20.3.0 Constant volume
20.0.6 Density of gases
20.4.0 Thermodynamics
20.0.0 Gas laws
Gas laws relate the pressure, temperature and volume of gas
4.220 Atmospheric pressure (experiments)
20.3.0 Constant volume, pressure law, p / T = constant
20.0.8 Dalton's law of partial pressures
4.8 Expansion of air
20.0.4 Gas pressure
20.0.9 Henry's law and decompression sickness, the
bends
20.0.3 Pressure law, constant volume
20.0.10 Standard atmosphere
20.0.6 Standard temperature and pressure, STP.,
density of gases
20.0.7 Universal gas equation, PV = nRT
20.1.0 Constant pressure, Charles' law (Gay-Lussac's law)
20.1.0 Constant pressure, Charles' law (Gay-Lussac's law) V1
/ T1 = V2 / T2, V / T = constant
20.1.01 Kinetic theory
20.1.1.5 Bicycle pump
4.9 Burn candle over water
6.35 Burn candle over water (Primary)
20.1.4 Burn candles over water (expansion of air
when heated)
20.1.1.6 Carbon dioxide gas
cylinder
20.1.1.1 Charles law, Use oil instead of mercury
for school Charles' law experiments
4.243 Cold air is heavier than warm
air, inverted paper bag balance
20.1.1.3 Expansion indicator
4.8 Expansion of air
20.1.1.4 Gas-filled bulb and U-tube manometer
20.1.2 Heat air and cool air
20.1.3 Heat flask with hands
5.42 Heated air expands (Primary)
20.1.1.2 Heated air expands
20.1.05 Hot air balloons
20.2.0 Constant temperature, Boyle's law (Mariotte's law)
20.2.0 Constant temperature, Boyle's law (Mariotte's law) P1V1
= P2V2, pV = constant
20.2.2 Air pump
4.230 Aneroid barometer, barograph
9.241 Breath volume
4.244 Scuba diving and Boyle's law
20.2.3 Lift weight by blowing, the work done by gas
pressure
4.229 Mercury barometer, barometric
pressure, atmospheric pressure
4.240 Model lungs
4.241 Oxidation and air pressure, steel
wool over water
4.223 Plastic syringes and air pressure,
Boyle's Law
20.2.4 Potato gun pneumatic launcher
20.2.1 Pressure effect on gas volume of syringe
4.238
Volume and pressure of air, Boyle's Law
20.3.0 Constant volume
Constant volume, pressure law, p / T = constant
12.3.3 Air has mass, air has weight, balance
balloons, weigh a basketball, coal gas has weight
24.2.4 Pressure and boiling point of water
20.0.3 Pressure law, constant volume
20.4.0 Thermodynamics
20.4.0 Thermodynamics, isothermal change and adiabatic change
23.11.0 Adiabatic processes
5.1.0.1 Avogadro's hypothesis, (Avogadro's
principle), Avogadro's number box
20.4.2 Crookes' radiometer
20.4.1 Heat cycles, Carnot cycle
20.4.7 Isothermal change and adiabatic change, Diesel
engine
20.4.01 Ice cubes in boiling water, second law of
thermodynamics
20.0.3 Pressure law, constant
volume
The pressure law states for a gas with constant volume the pressure is
proportional to the Kelvin temperature of the gas.
The volume occupied by one mole of gas at STP. = 2.24 X 10-2
m3.
20.0.4 Gas pressure
Gases are made up of molecules moving randomly at high speeds, in straight
lines, in all directions. Pressure is a measure of the force per unit area
on a surface. Pressure = Force / Area where force is in newton, N, and area
in square metres, m2. 1 newton / metre2 = 1 pascal,
Pa. The pressure of a gas = number of collisions per second per unit area
X the average impulse per collision for the molecules.
Standard pressure of one atmosphere, Pa = 1.02 X 105 N / m2.
20.0.5 Combined gas equation
The equations for Charles' law, Boyle's law and the Pressure law can be
combined as PV / T = constant (depending on the nature and the mass of that gas), or P1 × V1 / T1 = P2 × V2 / T2
Temperature, T, should be in absolute scale, Kelvin scale, K.
20.0.6 Standard temperature
and pressure, STP., density of gases
See: Saturation Vapour Pressure | See 5.1.3: Molar volume
STP refers to the standard conditions used in calculations of the effects
of changing temperature and pressure. They are STP. = 0oC or 273.15
K, and 760 mm Hg or 101325 pascals, Pa. (101.325 Nm-2).
The combined gas equations can be used to find the volume of a gas at STP,
i.e. at 0oC and 760 mm Hg pressure.
Density of gases at STP
Carbon dioxide 0.0019769 g / mL
Hydrogen gas 0.00008988 g / mL
Oxygen gas 0.0014290 g / mL
A standard atmosphere (International Standard Atmosphere), atm, is a hypothetical
atmosphere used as a basis of comparing altimeters. It is a pressure of 101.325
Nm-2, equivalent to the pressure exerted by a column of mercury
760 cm high at 0oC.
The density of a gas is inversely proportional to the absolute temperature provided the pressure remain constant
ρ2 / ρ1 = T1 /T2, where ρ = density and T = absolute temperature.
The density of a gas is directly proportional to the pressure if the temperature remain constant.
20.0.7 Universal gas equation
The universal gas equation combines the three gas laws as PV = nRT, where
P = absolute pressure in Pascals, Pa, V = volume gas in cubic metres,
m3, n = amount of gas in moles, R is the universal gas constant
(gas constant, molar gas constant, ideal gas constant, universal molar
gas constant) = 8.314 JK-1
mol-1, (8.314510), T = thermodynamic temperature, K (0oC + 273).
For the Boltzmann constant KB or K, N = number of particles, not moles, pV = NKBT
For specific gas constant, Rspecific = R / M (molar mass of the gas)
The van der Waals forces (Johannes Diderik van der Waals 1837-1923, Netherlands)
are the weak forces between molecules, including H bonding forces in H2O
and HF, dipole-dipole forces between HCl molecules and dispersion forces
between Cl and Cl. The van der Waals equation: (P + a / V2)(V-b) = RT, where a = mutual attraction constant between molecules, b = space occupied by molecules, and V = volume of the gas.
20.0.8 Dalton's law of partial
pressures
See: Saturation vapour pressure over water
The total pressure of a mixture of gases or vapours in a closed container
is equal to the sum of the partial pressures of each gas or vapour, i.e. the
sum of the pressures if each gas or vapour alone occupied the space in the
closed container. So each gas or vapour exerts its own pressure regardless
of the presence of any other gas or vapour. When a gas is collected over water,
the water molecules in the water vapour contribute to the total pressure over
the water.
Total pressure = pressure of gas produced + pressure of water vapour.
20.0.9 Henry's law and decompression
sickness, the bends
If the temperature is constant, the mass of gas dissolved at equilibrium
is directly proportional to the partial pressure of the gas. The solubility
of a gas depends directly on the gas pressure. The concentration of dissolved
gas depends on the partial pressure of the gas. If the pressure is doubled
the concentration of the dissolved gas double. If the temperature remains
constant increasing the pressure will increase the amount of dissolved gas.
O2 (g) <-->O2 (aq)
Pgas = KC, at constant temperature, where P = pressure, C = concentration
and K = the Henry's law constant that is different for every gas, temperature
and solvent.
The concentration to pressure ratio is the same when the pressure changes.
C1 / P1 =C2 / P2
Decompression sickness occurs when a person experiences a sudden change
in atmospheric pressure. Nitrogen has a low solubility in body fluids at
normal atmospheric pressure but at higher than normal pressure, additional
nitrogen molecules diffuse across the alveolar surfaces of the lungs and
into the bloodstream and tissues. If the atmospheric pressure then decreases
slowly, the excess nitrogen can diffuse out of the tissues, into the blood,
and across the alveolar surfaces without discomfort to the person. However
if the atmospheric pressure decreases suddenly, the nitrogen leaves solution
and forms bubbles of nitrogen gas in the blood, tissues, and body fluids.
Small bubbles fuse to form larger bubbles that twist tissues and produce
severe pain in joint capsules and causing the person to bend over, "the
bends". Treatment by recompression forces the nitrogen in the tissues back
into solution to alleviate the problem. Then a gradual reduction in pressure
allows the nitrogen to diffuse slowly out of the tissues without forming
bubbles. The bends still occurs to scuba divers who have dived too deep
or stayed too long at depth, to construction crews working in pressurized
surroundings and even to passengers experiencing a sudden loss of cabin pressure
in a commercial aeroplane, where a pressure experienced at 2000 metres height
is normally maintained.
20.0.10 Standard atmosphere
The standard atmosphere (USA, 1976 ) has following mean conditions at sea
level: pressure 101325 Pa, temperature 288.15 K (15 °C), density, ρ,
1.225 kg / m3, standard gravity, g = 9.90665 m /s2, R = 8.31432 JK-1
mol-1, and composition: N2 (78.084%), O2 (20.9476%), Ar (0.934%), CO2 (0.0314%), Ne (0.001818%), He (0.000524%), CH4
(0.0002%). However, the international standard atmosphere (ISA) used in international
weather data has conditions at sea level pressure 101325 Pa (1 atmosphere)
at 15oC with lapse rate -6.5oC / km and a range of different conditions for specific layers of the atmosphere.
20.1.0 Constant pressure, Charles' law (Gay-Lussac's
law) V1 / T1 = V2 / T2, V / T
= constant
See diagram 20.0.0: Contraction of gas obeying
Charles' law
(Jacques Charles 1746-1823) (Joseph Louis Gay-Lussac 1778-1850)
For a given mass of gas at constant pressure, the volume, V, is proportional
to the absolute or Kelvin temperature of the gas, T, Volume = constant ×
T, V / T = constant provided pressure is constant.
Volume is proportional to temperature, V1 / T1 = V2 / T2, where T = absolute
temperature. (Absolute zero = -273oC)
For a given mass of gas at constant pressure, the volume, V, increases
by 1/ 273 rd of its volume at 0oC for every Celsius degree rise
in temperature
Vt = Vo[1 + (1 / 273)t]
The new internal pressure, P2, of a litre of gas at 20oC enclosed
at pressure 770 mmHg, then heated to 100oC = P1 / T1 = P2 / T2,
(V1 = V2), 770 / 293 = P2 / 373, So P2 = 980 mm Hg
Charles' law (J. A. C. Charles 1746-1823: For a given mass of gas at constant
pressure, the volume is proportional to the absolute thermodynamic temperature,
K., V = KT. So all gases have the same coefficient of expansion at constant
pressure. However this is strictly true only at low pressures and high temperatures.
Gay-Lussac's law (J. L. Gay-Lussac 1808): When gases combine chemically,
the volumes of the reactants and the volume of the gaseous product bear simple
relationships to each other under the same conditions of temperature and pressure.
The effect of temperature on the volume of a gas
See diagram 20.1.0: Charles' law
V1 / T1 = V2 / T2 Constant
Pressure, volume / temperature graph, V / T = constant, PVT relationship,
Quantitative treatment of ideal gases. Boltzman's Constant, approximations
used for real gases
Put a drop of oil into the capillarity tube to seal a column of air. Measure
the length of the trapped column of air rather than its volume. Use a spring
band to fix a capillarity tube and a thermometer together, put them into a
beaker. Use the scale intervals on a thermometer to measure length. To read
easily, the lowest level of a column of air trapped in a capillarity tube
is better to meet at 0oC on the thermometer. Then record the length
of the column of air by using the scale nearest to top of the column of air.
Measure a set of values of length of a column of air and temperature between
0oC and 100oC. Before the experiment, mix crushed ice
and water in a bottle of mineral water, put them into a beaker. Record your
temperature readings in a suitable position of set up the table. Then pour
tap water into the beaker, heat it by an alcohol burner. As the temperature
reaches 40oC, 60oC, 80oC, record the length
of the column of air trapped in a capillarity tube each. Remove the alcohol
burner before taking records. As water boils, record the last reading. Draw
a graph of temperature t and length of the column of air L so your graph
can show how of volume of air varies with temperature.
20.1.01 Kinetic theory
The temperature of a gas is proportional to the mean kinetic energy of translation
of the molecules of the gas. Two gases at the same temperature have the same
mean kinetic energy.
The pressure of a gas is caused by the impact of its molecules on the wall of the containing vessel.
pressure, p = 1 / 3 nmVrms2, where p = pressure, m = mass of a molecule, n = number of molecules, Vrms = root mean square velocity
p = 1/3 ρVrms2, where ρ = density of the gas
The density of a gas is inversely proportional to the absolute temperature.
20.1.1.1 Use oil instead of mercury for school Charles'
law experiments
After Geoff Snowdon, The Australian Science Teachers Journal, Vol. 33 No.
2
Coloured oil can be put into a 30 centimetre length of capillary tubing
by using the following procedure: Leave both ends open. Heat the tube strongly
at one third the length. Dip an end into the oil. The oil rises into the tube.
Manipulate the tube to get a 5 cm length of oil. Seal an end or heat to seal.
20.1.1.2 Heated air expands
See diagram 20.1.1: Heated air expands
Fit a hard glass test-tube with a one hole stopper with glass tubing through
it. Invert the test-tube so that the end of the tubing is in a beaker of water.
Clamp the test-tube in that inverted position and heat it with a Bunsen burner.
Heat the test-tube and observe the bubbles from the end of the tube in the
beaker of water. Heat has caused the air to expand. Cool the test-tube by
pouring cold water over it. Water moves up the glass tubing as the cooling
air contracts. Fit a toy balloon over the neck of a small flask. Put the flask
in a container of water. Heat the water. The balloon expands as the heated
air in the flask expands.
20.1.1.3 Expansion indicator
See diagram 20.1.1.3: Expansion indicator
Use a piece of thick cardboard on a table as a base. Paste another piece
of cardboard vertically at the side of the base and mark it as a scale. Stretch
tight a rubber film over the mouth of a bottle to air proof the bottle. Flatten
one end of a drinking straw then paste it at the middle of the rubber film.
Cut the other end of the drinking straw into a sharp needle to act as an indicator.
Place the bottle on the base. Adjust the position of the bottle so that the
indicator points to half way up the scale. Observe the movement of the indicator
during the day. When heated the air in the bottle expands to press the rubber
film so that the indicator moves up.
20.1.1.4 Gas-filled bulb and U-tube manometer
Connect a glass bulb containing air or other gases to one arm of a manometer.
Place your hand over the bulb and observe the change in levels of the liquid
in the manometer.
20.1.1.5 Bicycle pump
Pump up a bicycle tyre and feel the increase in temperature. Measure the
decrease in volume of air in the pump during a pump stroke. The temperature
difference is very small for one stroke but if you keep pumping vigorously
you can feel the difference in temperature,
20.1.1.6 Carbon dioxide gas
cylinder
Open the valve and observer the formation of dry ice.
20.1.05 Hot air balloons
As the temperature of air in the balloon increases, its volume increases
to inflate and lift the balloon. A buoyant force, upthrust is due to the weight
of air displaced by Archimedes' principle. The density of air inside the
balloon is less than the density of the surrounding air. In 1783, J. A. C.
Charles, in Paris tested a balloon four metres in diameter containing hydrogen.
This experiment lead to Charles' law in 1787 later to be improved as Gay-Lussac's
law in 1809 by J. L. Gay-Lussac.
20.1.2 Heat air and cool air
See diagram 20.1.2: Heat conical flask
Use a 100 mL conical flask; a rubber stopper; a N-shape capillary of 250
mL length and a straight capillary longer than the height of the flask; a
400 mL beaker of coloured water. Add ink to the water.
20.1.3 Heat flask with hands
See diagram 2.1.3: Heat flask with hands
Use a small bottle or flask fitted with a stopper and inserted glass tube
that extends into the bottle. Put a small amount of oil in the glass tube
to trap air in the flask. Hold the flask in your hands. The oil moves up the
tube because the heat from your hands has expanded the air. The bottle will
change size first before you heat, or cooled the gas because the glass of
the bottle will expand. Cool the flask. The oil moves down.
Seal the flask with the rubber stopper. On the stopper insert the N-shape
capillary. Insert the other end of the N-shape capillary into the coloured
water at the beaker. Cover the flask with your hands to heating the air in
the flask. Observe the end of the capillary under the coloured water. Leave
your hands off the flask then hold the capillary. Observe the end of the
capillary under the coloured water again. While you heat the air in the flask,
its volume expands and pressure increases. So air bubbles appear at the end
of the capillary until the pressure inside the flask is equal to the outside
pressure. The amount of the air in the flask decreases at the process. While
the air in the flask becomes cold, the air pressure decreases to less than
the outside pressure so that the coloured water in the beaker under the
atmosphere pressure, enters the capillary to contract the air volume to
make the inside and outside pressures balance.
20.1.4 Burn candles over water
See diagram: 3.1.4.5: Burning candles | See diagram 4.9: Burning candle over water
1. Fill a trough with water and a float a burning
candle in it or attach burning candles to the bottom of the trough. Invert
a large beaker over the candle or candles. Note the level of the water inside
the beaker. At first the candle keeps burning and the volume of air inside
the beaker increases, caused by the heat from the candle., until some air
escapes from below the beaker to form bubbles in the trough. The candle flame
is extinguished when all the oxygen in the air inside the beaker is converted
to carbon dioxide and carbon monoxide and some smoke may issue from the wick
from the carbon of partially oxidized hydrocarbons. The level of the water
inside the beaker rises to above the original level.
2. Some decrease in volume will be caused by the candle wax burning to
form carbon dioxide and water. Some of the carbon dioxide will dissolves
in the water from the trough and the water vapour formed will condense to
form liquid water. More air escaped from the jar in the beginning due to
large amount of heat released by the two candles.
3. When we ignite the candle, the stearin (purified fatty acids) reacts
with oxygen (in excess) to produce carbon dioxide and water. The burning
causes air currents to shape the candle flame and ensure complete combustion
at the bottom and the outer surface of the flame. The hot air and products
of combustion rise up above the flame. When a jar is placed over the burning
candle the hot gases in the jar expand and pushing some of the air out of
the jar as bubbles in the water. As soon as the rim of the jar touches the
water, the burning occurs in a closed environment. Further pressing the jar
down into the water helps to retain the hot air in the jar under a pressure
greater than than atmospheric pressure and balanced by the pressure of the
depth of water.
4. The burning of hydrocarbon in the jar produces more molecules of carbon
dioxide and water than the molecules of oxygen consumed in the reaction.
The increased heat and number of molecules increases the pressure in side
as a result if not careful some bubbles of gas will escape from the jar. Over
the time the oxygen in the jar is reduced and conditions for burning are
changed. Burning under reduced oxygen may not produce carbon dioxide rather
a little carbon monoxide. When the candle is put out, the temperature decreases
followed by also a decrease in pressure due to condensation of water vapour
and decreased quantity of air due to thermal expansion during the process
of placing the jar on the candle. The overall situation is a decrease in
pressure inside the jar as compared to atmospheric pressure so despite water
being heavier that air, it is pulled into the jar. A negligible amount of
carbon dioxide is dissolved in the water during 30 - 40 minutes, the time
the experiment usually takes for performing in a classroom situation. If
the number of candles is increased in the jar, the heat produced is more therefore
more air is likely to escape from the jar due to thermal expansion during
the process of pacing the jar over them. Therefore, more water will rise
in the jar with more candles.
5. The nature and quantity of the products will depend upon the composition
of candle material. However it is assumed that combustion of saturated hydrocarbons
is taking place during burning. For the paraffins in the stearin candle, chain
length, n = about 30
During combustion the solid stearin combines with 3 volumes of oxygen gas
to form e volumes of carbon dioxide e gas + 2 volumes of water vapour
So the expansion of gases caused by this chemical reaction = 4/3 = 1.3'
2CH2 (s) + 3O2 (g)--> 2CO2 (g) + 2H2O
(g)
However after the candles are extinguished, drops of water appear on the
inside of the jar caused by condensation, so 3 volumes of oxygen have produced
2 volumes of carbon dioxide, a contraction of 2/3.
6. Previously, teachers taught (and some still teach) that the candle become
extinguished because all of the oxygen under the inverted jar "was used up",
i.e. converted to carbon dioxide, and so the decrease in volume of air under
the jar after the candles are extinguished indicating the proportion of oxygen
in the air. However some oxygen remains in the inverted jar as can be demonstrated
by testing with yellow phosphorus.
7. The rapid rise of water level in the jar after the candles are extinguished
is caused by decrease in pressure as the hot gases cool and the condensation
of water vapour. The amount of condensation of water will depend upon the
temperature difference between initial and final temperatures of the air in
the jar. Since air is above water, therefore saturated water vapour pressure
is considered in the beginning of the experiment. Increase in temperature,
during the candle burning, will make air unsaturated to accommodate additional
water vapours especially produced as a product of burning. A decrease in
temperature over time after the candle is off to the initial temperature
will help water vapour to condense. This condensation will decrease the pressure
inside the jar and will help water rise in the jar. The amount of water vapours
condensed during a small change of temperature as usually occurs in this
experiment may even be small to notice.
8. Some teachers believe that all the oxygen is consumed during combustion
before the candle is extinguished and the water rises in the jar to fill
in vacuum created by consumption of oxygen. They do not expect the air to
escape from the jar as a result of thermal expansion. They believe that one
candle will burn longer in the jar than two candles. The water level in jars
with one or two candles will rise to the same level because the amount of
oxygen in the jars is the same, about 20%.
9. A little carbon dioxide dissolves in the water during the experiment.
A jar full of carbon dioxide inverted over a trough of water does not completely
dissolve after some days. To study the level of water rise when the candle
was put out as soon jar touched the water, a floating candle was used and
it was made to sink as soon as jar touched the water in the trough. It was
found that water did rise to some extent, indicating that some air escaped
from the jar because hot air and burning products entered the jar from the
candle during the process of placing the jar over the candle. The oxygen in
the jar after the candle was extinguished produced rust in steel wool, reacted
with yellow phosphorus to produce white smoke of oxide and supported survival
of a mouse and insect for a long time. To test whether the presence of carbon
dioxide or lack of oxygen extinguishes the candle, remove the carbon dioxide
from the jar by using sodium hydroxide solution in the trough in place of
water. Also you can spray cotton wool with sodium hydroxide and attach it
to the bottom of the jar before it is inverted on the candle. The candle
burning time was almost doubled indicating that it is the presence of carbon
dioxide that extinguishes the candle. When a candle burning under a jar inverted
over water in a trough was repeated using two and three candles. The level
of water in the jar increased with an increase in number of candles. This
finding was used to emphasize that more oxygen is escaped from the jar before
or during the burning of candles. However it is not true that more oxygen
was consumed with the increase in the number of candles.
20.2.0 Boyle's law (Mariotte's
law)
PV = constant, if temperature is constant (from a pressure / volume graph)
Robert Boyle (1627-1691), (E. Mariotte 1620-1684) For a given mass of gas
at constant temperature, the volume is inversely proportional to the pressure,
PV = constant. The Boyle's law relationship would be true only for an ideal
gas with particles that occupy no space, have no forces between them, and
have perfectly elastic collisions between them and between the particles and
the walls of the container.
The pressure of a gas is caused by the gas particles colliding with the
walls of the container.
V1 / V2 = P2 / P1, P1V1 = P2 V2
The volume of a gas enclosed in a cylinder is halved when the piston is
pushed down half way. This action doubles the number of molecules per cubic
centimetre, so there are twice as many collisions with the walls of the cylinder
that causes the pressure to double.
P1V1 = P2 V2, 1 × 1 = P2 × 0.5, So P2 = 2.
20.2.1 Pressure effect on gas
volume of syringe
See diagram 20.1.3: Mounted syringe
Use a calibrated syringe mounted on a block of wood and with a platform
securely attached to the top of the plunger. Measure the masses of platform
and plunger, the outer diameter of the plunger or the inner diameter of a
syringe. Put light oil on the plunger to lubricate it. Lift the plunger,
record the original position of it. Seal the outlet with a piece of rubber
tube. Put weights on the platform and record volume of air in the cylinder
using the scale on the syringe. Change the weights on the platform, record
the volume of the air in the syringe under different case, but maintain the
temperature constant in this process. Calculate the air pressure. The pressure
acted on air in the syringe = atmospheric pressure + the pressure produced
by weights of plunger and platform + the pressure produced by weights added
on the platform. Observe and test according to measured volume and pressure
calculated. As the temperature is constant and the gas has a definite mass,
when its pressure increases its volume decreases, and vice versa. The product
of pressure and volume of the gas remains the same, i.e. PV = C. Finally,
graph the relationship between volume and pressure of air in the syringe.
20.2.2 Air pump
Use of a syringe needle may be not allowed in some school systems.
If temperature is constant, when you compress gas and reduce its volume,
its pressure will increase, and vice versa. Insert a piston covered with some
glycerine into a 100 mL pump with a valve. Rotate the piston inside the pump
several times to make the glycerine distributed evenly. This can insulate
the air inside the pump from outside completely. Open the valve and suck
up 60 mL air into the pump. Measure the volume of the air with the scale
on the pump. Close the valve to insulate the air in the pump from outside.
Push the piston to compress the air volume to about 2 / 3 of the original,
i.e. about 40 mL. Release the piston that will come back to the original position.
Pull the piston out with effort to expand the air volume in the pump to about
80 mL. Release the piston that will come back to the original position. The
reason of coming back of the piston is the pressure difference between two
sides of the piston. At constant temperature, the more the air volume inside
the pump is compressed, the more pressure it has. As the air volume expands,
the pressure decreases. When the piston is compressed, as the air pressure
inside the pump is higher than that of outside, the air inside the pump will
push the piston back to its original position. When you pull out the piston,
the air pressure inside the pump becomes less, the atmospheric pressure outside
pushes the piston back. You can do the experiment with a large glass syringe
instead of a pump. Close the hole with the fingers used as a valve.
20.2.3 Lift weight by blowing,
the work done by gas pressure
See diagram 20.2.1: Lift weight by blowing
20.2.4 Potato gun pneumatic launcher (pneumatic, Greek: pneuma, wind)
Be careful! This experiment, often called a spud gun, can be dangerous if
participants are not wearing safety goggles and if the metal tube is not
kept in a vertical position.
Use 2 m of 3 cm internal diameter metal piping and a 5 m wooden pole
< internal diameter of the metal piping. Secure the wooden pole
vertically in the ground with the length of the metal piping above the ground.
Push each end of the metal piping into a potato so that the cavity of the
metal tube is completely blocked. Hold the metal tube vertically above
the wooden pole. Hold the metal tube with both hands and push down quickly.
The potato plug flies out of the other end of the metal tube. The increase
of pressure on the air between the potato plugs causes expansion of the gases
between them. This application of Boyle's law is used in many more powerful devices, e.g.
dry ice gun, that have no place in a school science laboratory.
20.4.0 Thermodynamics, isothermal change
and adiabatic change
See diagram 20.4.0: Thermodynamics | See 2.0.5: Conic sections, hyperbola
Order online: Pressure Pumper kit,
clouds, refrigeration, air conditioning
1. An isolated system contains a certain quantity of energy called the
internal energy of the system = total kinetic energy and potential energy
of all the atoms and molecules in the system that can be transferred as heat.
Internal energy does not include chemical energy or nuclear energy. Thermodynamics
is about how energy changes from one form to another, the direction of heat
flow and how energy does work.
2. The value of the internal energy of a system can be changed by the following:
1. transfer of mass, 2. transfer of heat, 3. work done on or by the system.
In an isothermal change the temperature remains constant, and PV = a constant.
On a pressure / volume graph an isothermal change is shown as a rectangular
hyperbola.
3. In an adiabatic change no heat is is received or lost from the surroundings.
For an adiabatic system with constant mass, the transfer of heat = 0, the
change in internal energy = work done and a change in temperature occurs.
For example, if a piston is raised in a cylinder containing a gas, the volume
of the cylinder increases and the temperature of the gas falls as work is
done against the rising piston. On a pressure / volume graph an adiabatic
change is always steeper than a rectangular hyperbola because adiabatic expansion
is accompanied by a fall in temperature.
4. First law of thermodynamics: Heat can be changed into mechanical energy
and mechanical energy can be changed into heat energy but the total energy
of the system remains constant, i.e. the law of conservation of energy always
holds true.
5. Second law of thermodynamics: Heat cannot pass from a body at lower
temperature to a body at high temperature, heat always flows from hot bodies
to cold bodies, a machine unaided by an external agent cannot transfer heat
from a body at lower temperature to a body at higher temperature.
6. Third law thermodynamics: The entropy of a substance approaches zero
as is temperature approaches absolute zero. Entropy measure the unavailability
of the energy of a system to do work. In any closed system an irreversible
change is associated with an increase in entropy. For an adiabatic process
no heat transfer occurs and the entropy remains constant during the process.
Increase in entropy is another way of stating the second law of thermodynamics.
20.4.7 Isothermal change and
adiabatic change, Diesel engine
Order online: Fire Syringe, adiabatic
heating in diesel engine
For an ideal gas, i.e. no attractive forces between its molecules, the volume
decreases with temperature down to -273oC, called absolute zero
or 0o Kelvin, K. For monatomic gases, the molar heat capacity cp
= 12.5 joule / mole K, so you need 12.5 joules to raise the temperature of
a mole of a monatomic gas by 1K. In an isothermal change the temperature remains
constant. In an adiabatic change no heat is received from or lost to the
surroundings. Adiabatic expansion occurs when a gas expands quickly, or when
a gas is insulated from the surroundings. The gas does work and the temperature
drops, as in refrigeration. Adiabatic compression occurs when you compress
a gas quickly, or insulate a gas from the surroundings. The temperature rises,
as is used in igniting the fuel in a diesel engine.
20.4.01 Ice cubes in boiling
water, second law of thermodynamics
Heat a pot of water until it is boiling steadily. Add several ice cubes
to the pot. The boiling action stops almost immediately as heat is transferred
from the burner to the lower temperature ice rather than to the higher temperature
water. When all the ice is melted the boiling action starts again.
20.4.1 Heat cycles, Carnot cycle
Order online: Stirling
Engine, a closed cycle regenerative heat engine, low temperature differential
The working of an ideal reversible engine is shown as the Carnot cycle.
A gas is contained in a cylinder with a conducting base and nonconducting
walls and frictionless piston.
Stage 1: A constant heat source, temperature T1, heats the conducting base
and the load on the piston is decreased. Heat is taken in. Isothermal expansion
of the gas at temperature T1 occurs.
Stage 2: The heat source is removed, the conducting base of the cylinder
is insulated and the load on the piston is decreased. Adiabatic expansion
of the gas occurs as the temperature of the gas falls to T2. Work is done
by the gas.
Stage 3: The conducting base of the cylinder is no longer insulated, it
is heated by a constant heat source, temperature T2 and the load on the piston
is increased. Heat is given out. Isothermal compression of the gas at temperature
T2 occurs. Work is being done on the gas.
Stage 4: The heat source is removed, the conducting base of the cylinder
is insulated and the load on the piston is increased. Adiabatic compression
of the gas occurs until the temperature returns to T1. Work is done on the
gas
No engine can be more efficient than the theoretical reversible engine
working between the same temperature limits, (T2 - T1).
20.4.2 Crookes' radiometer
See diagram 20.4.2: Crookes' radiometer
Order online: Radiometer, (Crookes'
radiometer), sun-powered rotation
The Crookes radiometer was invented by Sir William Crookes in 1873 but
he mistakenly thought it measured the pressure of light. It consist of a
paddle wheel of vertical mica paddles with alternate surfaces white or black
connected by a vertical spindle in a partly evacuated glass container. It
spins with the white sides approaching the source of radiation. Increasing
the radiation increases the speed of turning. Maintaining the level of radiation
but decreasing the temperature reverses the direction of rotation. Gas molecules
move from the cold white side to the warmer black side causing the cold white
side to move forward. Also, gas molecules hitting the edges of the warmer
sides bounce off the paddle with increasing speed causing the slight increase
in temperature of the black sides, so these rebound molecules increase in
speed. Crookes' radiometer is still sold in novelty shops as a "light mill".
23.11.0 Adiabatic processes
See 20.4.0: Thermodynamics
In an isothermal change the temperature remains constant. In an adiabatic
change no heat is received from or lost to the surroundings so there is a
transfer of energy into or out of the system in the form of work only, e.g.
very rapid expansion of a gas or any process in an insulated container.
1. Light a match head
Push down hard on a piston in a close fitting cylinder to ignite a match
head at the bottom of the cylinder.
2. Expansion cloud chamber
2.1 Put some smoke and alcohol in a stoppered flask and shake. When the
stopper is released a fog forms.
2.2 Apply pressure to a flask containing saturated water vapour then release
the pressure. No changes are observed. Repeat the experiment by adding smoke
to the water vapour. On releasing the pressure a cloud forms in the flask.
4. Adiabatic cooling
4.1 Pressurize a one gallon jar with a bicycle pump until the cork blows.
Measure the temperature of adiabatic heating and cooling. A
4.2 n air cylinder moves a piston back and forth. Use a thermocouple to
measure the temperature of adiabatic heating and cooling.
5. Expansion chamber
Make a temperature detector to insert into a flask that will be warmed
and cooled by compression and expansion of air in the flask
6. Joule-Kelvin coefficients
Use a thermocouple to measure the temperature change as cools on expansion
and heats on expansion.