Explanation Gas pressure is caused by collisions of gas molecules on the wall of the container. The molecule collide with one other , with the walls of the container and with the surface of the piston in elastic collisions. The collisions of air molecules with the walls of the syringe and with the surface of thumb or the piston resulting in force acting on them. When the gas molecule hits the surface of the wall of syringe with a velocity, v and bounces back with velocity ,-v there is a change of momentum.

According to the Newton’s Second Law of motion, force equals to rate of change of momentum. Hence, there is a force, F acting on the wall of the syringe. P = F / A Therefore, there is a pressure exerted on the wall of the container.

Existence of Gas Pressure The plastic bottle expands after it has been exposed to sunlight. Why? This is due to the volume of air in the bottle increases when the temperature increase. The lid of the tin will bursts open when the heat energy is supplied to it. Why? This is because the air pressure in the tin increases when the temperature increases. When a balloon is compressed, the balloon is not flattened and a resistance is felt. Why? This due to the air pressure in the balloon increases when volume is decreased.

At the end of this lesson, you should be able to: GAS LAWS At the end of this lesson, you should be able to: Explain gas pressure, temperature and volume in terms of the behaviour of gas molecules. Determine the relationship between Pressure and volume Volume and temperature Pressure and temperature For a fixed mass of gas. Explain absolute zero Explain the absolute/kelvin scale of temperature Solve problems involving pressure, temperature and volume of a fixed mass of gas.

Property of gases There is a relationship between pressure, volume and temperature of a gas. For a gas in an enclosed container, the Number of molecules is constant Mass of the gas is constant Behaviour of the gas depends on the volume, temperature and pressure of the gas.

Pressure of a gas According to the kinetic theory, a gas consists of a large number of molecules that are constantly moving at random with high speeds. During collisions, a molecule exerts force on the wall. The momentum change during a collision dp = mvx- (-mvx) = 2mvx Thus, the pressure of a gas is due to the collisions of the gas molecules with the walls of the container. Gas pressure can be increased by: Increasing the temperature Reducing the volume Increasing the number of molecules. -mvx mvx

Volume of gas The volume of gas is the space occupied by its molecules. Therefore, the average distance between the gas molecules determines its volume. The volume of the gas is equal to the volume of the container.

Temperature of gas Gas molecules are in constant random motion and have kinetic energy. When gas is at higher temperature, the gas molecules move with a greater velocity and will have more kinetic energy. The temperature of the gas is related to the average kinetic energy of the gas molecules.

GAS LAW BOYLE’S LAW CHARLES’ LAW PRESSURE LAW

Gas law Boyle’s Law Boyle’s law states that the pressure of a fixed mass of gas is inversely proportional to its volume if the temperature is kept constant. The mathematical expression for Boyle’s law is or While temperature kept constant P1V1 = P2V2 P V Pressure against volume

When the volume of a gas is decreased, the number of molecules per unit volume increases The same number of molecules moves in a smaller space The molecules collide more frequently with the walls of the container The increase in the rate of collisions results in an increase in the pressure exerted by the gas

Example The air in the cylinder of hand pump has a initial volume of 800 cm3 and pessure 102 kPa. The air is then slowly compressed to a volume of 160 cm3. What is the pressure of the compressed air in the pump? Answer P2 = 510 kPa

Gas law Charles’ law Charles’s law states that the volume of a fixed mass of gas is directly proportional to its absolute temperature if the pressure is kept constant. The mathematical expression for Charles’ law is V α T While pressure is kept constant V = constant T or V1 = V2 T1 T2 V(cm3) T (K) Volume against temperature

When the temperature of a gas is increased, the speed of its molecules increases Since the speed of the molecules increase with temperature, the force that acts on the walls of the container will be greater if its volume remained unchanged As a result, the volume of a fixed mass of gas will increase when its temperature is increased, provided that the pressure remains constant

Example 2.4 m3 of air at 27 °C in an expandable cylinder is heated to a temperature of 87 °C at constant pressure. What is the new volume of air? Answer V2 = 2.88 m3

Gas law Pressure law The pressure law states that the pressure of a fixed mass of gas is directly proportional to its absolute temperature if the volume is kept constant The mathematical expression for the pressure law is P α T That is P1 = P2 when volume kept constant T1 T2 P (Pa) T (K) Pressure against temperature

When a gas is heated, the average kinetic energy of the molecules increases. The temperature of the gas increases The faster moving molecules strike the walls of the container more frequently The molecules also experience a larger change of momentum when the bounce back from the walls A larger force is exerted on the walls resulting in a higher pressure

Example The initial pressure and temperature of the air in a car tyre was 200 kPa and 27° C respectively. After a journey, the pressure of the air was found to be 230 kPa. Calculate the temperature of the air in the tyre. Answer T2 = 345 K = 345 – 273 = 72 °C

Absolute temperature and the Kelvin scale In the experiment to verify Charles’ Law, the graph of V α T is a straight line which cuts the temperature axis (T) at the value -273°C. The value -273°C is equivalent to 0K and known as the absolute zero because it is the lowest possible temperature to be reached.

If the absolute zero is taken as the origin, the temperature scale is known as the absolute scale or Kelvin scale. The temperature in this scale is known as the absolute temperature and its unit is the Kelvin (K). The relationship between the temperature in the Celcius scale and Kelvin scale is as follow: t °C = (Ø + 273 ) K Ø K = (t – 273 ) °C Where t = temperature in the Kelvin scale. Ø= temperature in the Celcius scale

The combined gas law For Boyle’s Law , PV = constant For Charles’ Law, V / T = constant For Pressure Law, P / T = constant When combine all the equation, PV / T = constant P1V1 = P2V2 T1 T2 P V T

Problem solving