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The Gas Laws Lesson 1 : Boyle’s Law Lesson Objectives • State the relationship between the pressure and volume of a fixed mass of gas, at constant temperature • P∝1/V or P1V1 = P2 V2 • Carry out calculations using this relationship Pressure and Volume Low P, large V P x V is constant High P, small V Boyle’s Law • For a fixed mass of gas at a constant temperature, the volume of the gas is inversely proportional to the pressure • If the pressure is doubled, the volume is halved; if the pressure is tripled, the volume is reduced to one-third, etc. • This can be mathematically written in these three ways: • P ∝ 1 / V P x V = constant P1V1 = P2 V2 • This relationship is called Boyle’s law Boyle’s Law Experiment • This is the demonstration you will see to investigate Boyle’s Law Volume scale Gas (air) Pressure Gauge P – V Graph P∝1/V • This is the typical curve for two variables which are inversely proportional to each other A moving version! P∝1/V (cm3) (Pa) Note : the temperature is constant! A More Tricky graph…. P (Pa) P∝1/V 1/V (1 / cm3) • If you plot a graph of P against 1 / V, you will get a straight line through the origin. This is the proof that P and V are inversely proportional Some Results Pressure (kPa) Volume (cm3) 50 1000 100 500 150 330 200 250 250 200 1/V Use these results to get P – V and P - 1/V graphs like the ones in the previous slides Boyle’s Law The volume of a gas is inversely proportional to its pressure if temperature is constant Robert Boyle Try Some Questions 1. A bubble of air released by a SCUBA diver has a volume of 6cm3 when released under water where the pressure is 3 atmospheres (300 kPa). What is the volume of the bubble when it reaches the surface where the pressure is 1 atmosphere (100 kPa)? 2. The fuel mixture in the cylinder of a car engine has a volume of 400cm3 at a pressure of 100kPa. It is then compressed until its volume is reduced to 50cm3. What is the new pressure? Lesson 2 : The Pressure Law Lesson Objectives • State the relationship between the pressure and temperature of a fixed mass of gas, at constant volume (s) • P∝T or P1 / T1 = P2 / T2 (s) • Carry out calculations using this relationship (s) • Explain how this relationship leads to the kelvin temperature scale (s) • Convert between temperatures in kelvin and °C (s) Pressure Law Constant volume Low particle energy High particle energy • The pressure of a gas increases when the temperature increases, if the volume stays constant Pressure law Pressure Law apparatus • This is the apparatus used to investigate the relationship between temperature and pressure of a gas at constant volume Pressure-Temperature Graph • If temperature is in °C the graph is linear, but not through the origin At -273°C the pressure (theoretically) would be zero. This means that the particles have zero kinetic energy. - 273°C P (kPa) T (°C) Kelvin Temperature Scale • The pressure-temperature graph suggests that a true zero of temperature is at -273°C • This is known as absolute zero • Lord Kelvin used this to invent a new scale of temperature called the kelvin scale • Absolute zero is zero kelvin (0K) which is the same as -273°C • To change temperatures from °C to K you add 273 • To change temperatures from K to °C you subtract 273 Kelvin and Celsius Try These Change these to kelvin 1. 0°C 2. 100°C 3. 27°C 4. -20°C Change these to °C 1. 0K 2. 100K 3. 273K 4. 1000K Answers : Answers : 1. 2. 3. 4. 1. 2. 3. 4. 273K 373K 300K 253K -273°C -173°C 0°C 727°C Another P – T Graph • If the temperature is measured in kelvin, the graph passes through the origin • In other words, pressure is directly proportional to temperature (in kelvin) P (Pa) P∝T T (K) The moving version! (Pa) (K) P∝T The Pressure Law • For a fixed mass of gas at a constant volume, the pressure of the gas is directly proportional to the temperature (in kelvin) • If the temperature is doubled, the pressure is doubled; if the temperature is tripled, the pressure is tripled, etc. • This can be mathematically written in these three ways: • P ∝ T P ÷ T = constant P1 ÷ T1 = P2 ÷ T2