Topic 5 Kinetic theory and gases Unit P3: Applications of physics Topic 5 Kinetic theory and gases Student Notes

Unit P3: Applications of physics Kinetic theory and gases W.A.L.T We Are Learning To Unit P3: Applications of physics Topic 5 Kinetic theory and gases 5.1 Use a simple kinetic theory model to describe movement of particles in the three states of matter 5.2 Explain the pressure of a gas in terms of the motion of its particles 5.3 Describe the effect of changing the temperature of a gas on the speed of its particles

States of matter – a particle view solid liquid gas Close packed in a regular pattern, occupy least space Particles (molecules) slightly further apart than in solids Very far apart and occupy any available space Vibrate about fixed positions Particles slide past one another Move randomly at high speed Held by very strong attractive forces Attractive forces between particles (inter-molecular forces) Weak forces of attraction between particles

Moving particles Solid Gas Liquid gas condenses cooling liquid freezes heating liquid boils solid melts heating If a gas is cooled down its molecules have less energy and move more slowly. If it is heated up they have more energy and move faster. This idea about moving molecules is called the kinetic theory. Further cooling causes condensation into a liquid and eventually freezing into a solid. Heating a solid causes it to melt and a liquid to evaporate.

Pressure Pressure = Force Area

In this topic we will be investigating how the volume, temperature and pressure of a gas are related to each other. Volume: how much space a gas occupies Temperature: a measure of how hot or cold the gas is Pressure: The force exerted per unit area. The pressure of a gas is caused by its particles hitting the walls of its container. The more frequent the collisions and the harder they hit the greater the pressure.

Unit P3: Applications of physics Kinetic theory and gases W.A.L.T We Are Learning To Unit P3: Applications of physics Topic 5 Kinetic theory and gases 5.9 Investigate the volume and pressure relationship for a gas 5.10 Use the relationship: V1P1 = V2P2 to calculate volume or pressure for gases of fixed mass at constant temperature

Boyle’s law For a fixed mass of gas, the pressure is inversely proportional to the volume if the temperature remains constant. V1P1 = V2 P2

Example: A diver uses an air bag to lift an antique cannon from the seabed. At the seabed, the volume of the air in the bag is 0.5 m3. The pressure at the seabed is 300 kPa, the pressure at the surface is 100 kPa. The temperature does not change. What is the volume of the air bag when it reaches the surface of the sea? V1P1 = V2P2 0.5 x 300 = V2 x 100 150 = V2 x 100 150 = V2 100 V2 =1.5m3 At the surface, the volume of the air bag is 1.5 m3

Unit P3: Applications of physics Kinetic theory and gases W.A.L.T We Are Learning To Unit P3: Applications of physics Topic 5 Kinetic theory and gases 5.7 Investigate the temperature and volume relationship for a gas 5.4 Describe the term absolute zero, -273°C, in terms of the lack of movement of particles

Investigating the temperature and volume relationship of a gas heat

Absolute zero The temperature -2730C is called absolute zero. This is the temperature at which the pressure of a gas would be zero and the particles would not move.

Unit P3: Applications of physics Kinetic theory and gases W.A.L.T We Are Learning To Unit P3: Applications of physics Topic 5 Kinetic theory and gases 5.5 Convert between the Kelvin and Celsius scales 5.6 Recall that the average kinetic energy of the particles in a gas is directly proportional to the Kelvin temperature of the gas

Convert between the Kelvin and Celsius scales Convert 27 0C, -3 0C, 150 0C and -90 0C to Kelvin 27 0C -3 0C 150 0C -90 0C 300 K 270 K 423 K 183 K Convert 373 K, 200 K and 1000 K to Celsius 373 K 200 K 1000 K 100 0C -73 0C 727 0C

Kinetic energy of the particles in a gas If you double the kelvin temperature, the average kinetic energy of the particles in a gas also doubles. Directly proportional!

Unit P3: Applications of physics Kinetic theory and gases W.A.L.T We Are Learning To Unit P3: Applications of physics Topic 5 Kinetic theory and gases 5.8 Use the relationship: V1 = V2T1/T2 to calculate volume for gases of fixed mass at constant pressure (rearranging not required)

Charles’ law Charles’ law states that if a given quantity of gas is held at a constant pressure, its volume is directly proportional to the absolute temperature (Kelvin). V1 = V2T1 T2 NOTE: Temperature must be in Kelvin (K)

Question A hot air balloon contains 2000 m3 of air at 1000C. What volume of air at 50C is needed to fill the balloon? V1 = V2T1 T2 1000C 50C 373K 278K V1 = 2000 x 278 373 1491 m3

Unit P3: Applications of physics Kinetic theory and gases W.A.L.T We Are Learning To Unit P3: Applications of physics Topic 5 Kinetic theory and gases 5.11 Use the equation: initial pressure (pascal, Pa) x initial volume (metre3, m3) / initial temperature (kelvin, K) = final pressure (pascal, Pa) x final volume (metre3, m3) / final temperature (kelvin, K) P1V1/T1 = P2V2/T2 5.12 Apply an understanding of the equation in 5.11 to the use of bottled gases in medicine, including the need for a pressure above atmospheric and the calculation of the volume of gas released at atmospheric pressure

P1V1 = P2V2 T1 T2 Combined gas law Note: P1 initial pressure (pascal, Pa) V1 initial volume (metre3, m3) T1 initial temperature (kelvin, K) P2 final pressure (pascal, Pa) V2 final volume (metre3, m3) T2 final temperature (kelvin, K) Note: When using this equation, temperature must be in Kelvin!

Example: A diver uses an air bag to lift an antique cannon from the seabed. At the seabed, the volume of the air in the bag is 0.5 m3. The pressure at the seabed is 300 kPa, the pressure at the surface is 100 kPa. The temperature does not change. What is the volume of the air bag when it reaches the surface of the sea? P1V1 = P2V2 T1 T2 P1 = 300 kPa P2 = 100 kPa V1 = 0.5 m3 V2 = ? T1 = T2 300 x 0.5 = 100 x V2 150 = 100 x V2 150 = V2 100 V2 = 1.5 m3 (At the surface, the volume of the air bag is 1.5 m3.)

Air particles are moving (they have kinetic energy) .. they are colliding with walls of the balloon… … exerting a force 0 C 273 K -273 C 0K 290

P1V1 = P2V2 T1 T2 101 x 2.10 = 102 x 2.20 290 T2 306.8

Gases take up large volumes at atmospheric pressure and so they need to be compressed and stored a higher pressures.

Gases take up large volumes at atmospheric pressure and so they need to be compressed and stored a higher pressures.

P1V1 = P2V2 T1 T2 240 litres P1V1 = P2V2 2 x 106 x 12 = 1 x 105 x V2 The pressure of Helium gas in a canister is 2.0 x 106 Pa and its volume is 12 litres. Once the gas is released at normal air pressure (1 x 105 Pa) how much volume will it occupy? Assume the temperature of the gas doesn’t change. P1V1 = P2V2 T1 T2 P1V1 = P2V2 2 x 106 x 12 = 1 x 105 x V2 2.4 x 107 = 1 x 105 x V2 2.4 x 107 = V2 1 x 105 240 litres