Higher Physics – Unit – Gas Laws

Kinetic Theory of Gases The kinetic model of matter explains the behaviour of gases using a model. The model considers gases to be made up from a large number of very small particles which are far apart, move randomly at high speeds and collide (elastically) with everything they meet. Volume The volume of a gas is taken as the volume of the container. The volume occupied by the particles themselves is so small it is neglected.

Temperature The temperature of a gas depends on the kinetic energy of the gas particles. The faster the particles move the greater their kinetic energy and the higher the temperature. Pressure Pressure of a gas is due to the particles colliding with each other and the walls of the container. The more frequent and harder the collisions, the greater the pressure.

Boyles Law Pressure and Volume The pressure of a fixed mass of gas is inversely proportional to its volume. This is used in the form: pressure (Pa – Pascal) volume (m 3 ) ** NOT ON DATA SHEET **

Graphs of Relationship pressure volume What remains constant throughout? temperature of gas, mass of gas. pressure

Example 1 A sample of gas has a volume of 30 cm 3 at a pressure of 2x10 5 Pa. Calculate the new volume of gas when the pressure is increased to 5x10 5 Pa.

Worksheet – Boyle’s Laws Q1 – Q5

Pressure Law Pressure and Temperature A fixed mass of gas at a constant volume is considered. If the temperature is increased, the particles move with greater speed and kinetic energy. Collisions are more frequent and severe, causing pressure to increase. When the temperature is decreased, the particles move with less speed and kinetic energy. Collisions are less frequent and severe causing pressure to decrease.

Graph of Relationship The result is a straight line that does not pass through the origin. p T / o C -273 When the graph is extended back until the pressure reaches zero, it crosses the axis at -273°C. This is known as absolute zero. When the pressure is graphed against temperature in kelvin, the graph shows pressure to be directly proportional to temperature. NOT directly proportional directly proportional

Relationship The pressure of a gas is directly proportional to its temperature – IN KELVIN. This is used in the form: pressure (Pa – Pascal) temperature (K) ** NOT ON DATA SHEET ** When using this equation – temperature must be in kelvin (K).

What remains constant throughout? volume of gas, mass of gas.

Absolute Temperature The lowest possible temperature is -273°C. This temperature is called absolute zero. The absolute temperature scale calls -273°C, zero kelvin (K). Converting °C to K add 273 Converting K to °C subtract 273 An increase of 5°C = an increase of 5 K. No negative temperatures on the kelvin scale.

Pressure At Absolute Zero At absolute zero, the pressure is zero. This is because the particles do not move at absolute zero, so there are no collisions with the container walls. Hence, there is zero pressure.

Pressure Law Problems Example 1 A quantity of gas has a pressure of 2.5x10 5 Pa at a temperature of 20 °C. (a)Calculate the new pressure when the temperature reaches 37 °C. (b)State two important assumptions made in part (a).

(a) (b) Two important assumptions are that: the mass of gas is fixed, the volume of gas is fixed.

Worksheet – The Pressure Law Q1 – Q7

Charles’ Law Volume and Temperature A fixed mass of gas at a constant pressure is considered. If the temperature increases, the particles move with a greater speed and kinetic energy. The volume increases. If the temperature decreases, the particles move with less speed and kinetic energy. The volume decreases.

Graph of Relationship The result is a straight line which does not pass through the origin. V T / o C -273 When the graph is extended back until the volume reaches zero, it crosses the axis at -273°C. When the volume is graphed against temperature in kelvin, the graph shows volume to be directly proportional to temperature. NOT directly proportional directly proportional

Relationship The volume of a gas is directly proportional to its temperature – IN KELVIN. This is used in the form: volume (m 3 ) temperature (K) ** NOT ON DATA SHEET ** When using this equation – temperature must be in kelvin (K).

Example 1 There is 50 cm 3 of gas at 27 °C collected. Calculate the volume of gas at 10 °C when the pressure is unchanged.

Worksheet – Charles’ Law Q1 – Q7

Combined Gas Equation Pressure, Volume and Temperature In combining Boyle’s Law, the Pressure Law and Charles’ Law we can get one relationship that relates pressure, volume and temperature of a fixed mass of gas.

pressure (Pa) ** NOT ON DATA SHEET ** When using this equation – temperature must be in kelvin (K). This equation is used in the form: temperature (K) volume (m 3 )

Gas Laws and Kinetic Theory Pressure and Volume (Mass and Temperature Constant) As volume decreases Gas particles are closer together Particles hit walls of container more often Over a smaller area So the pressure of the gas increases: Repeat for volume increase.

Pressure and Temperature (Mass and Volume Constant) As temperature rises The gas particles move faster They hit walls of the container more often and with greater force (harder) So the pressure of the gas increases: unchanged Repeat for temperature decrease.

Volume and Temperature (Mass and Pressure Constant) As temperature rises The gas particles move faster They hit walls of container with greater force (harder) For constant pressure – volume must increase This gives bigger area The pressure of the gas remains unchanged: Repeat for temperature decrease.

Worksheet – Combined Gas Equation Q1 – Q10