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4.4 UNDERSTANDING THE GAS LAWSThe behaviour of gas depends on three properties of gas

1) Volume2) Temperature3) Pressure1) VOLUME OF A GASthe molecules move freely in random motion and fill up the whole containerthe volume of gas = volume of the container

2) temperatureThe molecules are in continuous random motionWhen the temperature of gas is raised, the average kinetic energy of gas molecules increasesThe average kinetic energy is proportional to the temperature3) pressureThe molecules are in continuous random motion.When a molecule collides with the wall of the container and bounces back, there is a change in momentum and a force is exerted on the wallThe force per unit area is the pressure of the gas

Property and symbolSI unitSymbol for SI unitOthers unitPressure, PpascalPaNcm-2, cm HgVolume, V(metre)3m3mm3, cm3Temperature, T kelvinKC, FSet up the apparatus as shown in the figure aboveThe initial volume of the air in the syringe is adjusted to a volume of 120 cm3 .Record the pressure from the Bourdon gaugeThe piston is gently applied to push the air into the syringe to a volume of 100 cm3. Record the pressureRepeat for different values of volume

ACTIVITYRESULTSVolume, V ( cm3)Pressure, P (Pa)120100806040RELATIONSHIP BETWEEN PRESSURE AND VOLUMEThe volume of container A is biggerThe number of gas molecules per unit volume is lowThe gas molecules collide with the container less frequentlyAs the result, the pressure is lower

A BThe volume of container B is smallerSo, the number of gas molecules per unit volume is highThe gas molecules will collide with the walls of the container more frequentlyAs the result, the pressure in the container is high

A Bboyles lawBoyles law states that for a fixed mass of gas, the pressure of the gas is inversely proportional to its volume when the temperature is kept constant

P inversely proportional to V PV = constant or P1V1 = P2V2

EXAMPLEA bubble of air is formed at the base of the lake. At the moment, its volume is 30 cm3 and it experiences a pressure of 190 cm Hg. What is the volume of the bubble when it reaches the surface of the sea? The atmospheric pressure = 76cm Hg

solution:P1V1= P2V2(190)(30) = (76) V2

V2= 75cm3summary

DEMONSTRATION

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RELATIONSHIP BETWEEN VOLUME AND TEMPERATUREWhen the temperature of gas is raised, the kinetic energy of molecules increase. the molecules move fasterThe molecules push the pistonThe gas expands and the pressure remains constant

extrapolating the v- graph The volume of a gas decreases when its temperature is lowered.Impossible to lower the temperature until the volume becomes zero

absolute zero The lowest possible temperature that is -273C (0 Kelvin / 0 K) is known as the absolute zero of temperature

The gas theoretically stop moving and have zero volume

The temperature measured in Kelvin scale is called as the absolute temperatureGraph volume vs temperature (kelvin scale )The volume is directly proportional to the temperature of gas

TemperatureCelcius scaleKelvin scaleAbsolute zero-273C0 KIce point0C273KSteam point100 C

373 KUnknown temperature C

(+ 273) Kcharles law Charless law states that for a fixed mass of gas, the volume of the gas is directly proportional to its absolute temperature when its pressure is kept constant

mathematical expression V T

V/ T = constant

SIMULATION !!!!!!

example The figure shows a balloon filled with air at temperature of 30C. The same balloon is then filled with air at a temperature of 50C. What id the final volume of the balloon if its initial volume is 20cm3 ?

Solution:

V1= 20cm3 T1= (30 + 273) =303KV2 = ? T2= (87 + 273) =360K

V1/ T1 = V2 / T2 20/303 = V2 / 323 V2 = 21.3 cm3QUESTION1) What is the formula for Charless Law?

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2) Which of the following situations involved Charles Law?

A: Air pressure in a soccer ball increases during a hard kick

B: The size of bubble in the dough increases when it was bake in an oven

C: Gas pressure increases after a gas cylinder was put under the sunlight

D: Helium gas balloon expanded when it goes up the sky

summary

SIMULATION

4.4 UNDERSTANDING THE GAS LAWSrelationship between pressure and temperatureIn container A, the temperature of gas is lowThe gas molecules have low kinetic energy and move at low speed.Thus, the frequency of collisions between gas molecules and the wall is low.The pressure is low

ABIn container B, the temperature is higherThe average kinetic energy of the gas molecule is highThus, higher frequency of collision between the gas molecules and the walls of the containerThe pressure in container B is greater

ABextrapolating graph of Pressure vs temperature

graph of pressure vs absolute temperature

pressure law The pressure law states that for a fixed mass of gas, the pressure of the gas is directly proportional to its absolute temperature when its volume is kept constant

mathematical expression P T

That is P / T = constant

or P1 / T1 = P2 / T2EXAMPLE The air pressure in a bicycle tyre is 150kPa at a temperature of 30C. What is the air pressure in the tyre at a temperature of 33C? [Assume the volume of the air in the tyre is constant]

Solution: P1=150kPa T1 = 30 + 273 = 303 K P2 = ? T2 = 33 + 273 = 306 K

P1 / T1 = P2 / T2 150/303 = P2 / 306

P2 = 151.5 kPa

QUESTION The initial pressure and temperature of the air in the car tyre was 200 kPa and 27C respectively. After a journey, the pressure of the air was found to be 230kPa. Calculate the temperature of the air in the tyre.

Solution:

SOLUTION P1 = 200 kPa T1=(27+273) =300K P2 = 230 kPa T2 = ?

using pressure law,

P1 / T1 = P2 / T2

200/300 = 230/ T2

T2 = 230 x 300 200 = 345 K