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The Ideal Gas Law The Ideal Gas Law Of the three phases of matter, solid liquid and Putting all these dependencies together, we can gas, the simplest to understand is gas. This is write an equation for the pressure of the gas in because the particles that make up a gas, atoms the box. and molecules, simply rattle around like ping pong balls in a vigorously shaken box. = 푛푅푇 푃 We see that pressure is 푉proportional to the temperature of the gas, and to , the number 푃 of moles of gas particles. It’s also inversely 푇 푛 proportional to , the volume of the box. is the constant of proportionality. We call it the 푉 푅 universal gas constant. The equation is usually written this way. = This is called the Ideal푃푉 Gas푛푅푇 Law. The remarkable thing about this equation is that it holds for all gases, whether it’s air, hydrogen The balls bounce against the inside of the box, gas, carbon dioxide, or whatever. It even holds imparting tiny impulses so that together they for the gas that makes up the Sun and all other exert a force on each wall. The amount of force stars, and the gas between stars that comprises per unit area is what we call pressure. most normal matter in the universe. The pressure that’s exerted (whether it’s ping The Number of Gas Particles in a Gallon of Air pong balls or gas particles) is proportional the Let’s use the Ideal Gas Law to make a number of particles in the box. calculation: the number of gas particles in a It’s also dependent on the speed that each gallon of air at the surface of the Earth. We’ll particle is moving. The temperature of a gas is use the above equation to find , the number of a measure of the speed that the particles are moles of gas, and knowing this we can find the 푛 moving, and it turns out that the pressure is number of gas particles. proportional to the temperature. At the Earth’s surface, the atmosphere pressure The pressure also depends on how big the box is about 101,000 Newtons per square meter is: how much space the particles are allowed to (101,000 / ). That’s the pressure in the move around in. The smaller the box, the more equation. Converting2 one gallon to SI units we 푁 푚 푃 particles there are in a given volume of space, get about 3.79 × 10 . This is , the and the higher the pressure. As a result, the volume. Room temperature−3 3 is around 22 , but 푚 푉 pressure is inversely proportional the volume of we need to express this in absolute units (Kelvin 퐶 the box. temperature scale). This is about = 295 . 푇 퐾 The constant = 8.31 in SI units. We can It’s ignited by the spark plug, and the hot gases insert these values into the ideal gas law. expand, pushing the piston and turning the 푅 crankshaft. You can see why the gas expands = by looking at the Ideal Gas Law. (101,000 / )(푃푉3.79 ×푛푅푇10 ) = 2= (8.31 /(−3 3 ))(295 ) 푁 푚 푚 If the temperature 푃푉of the푛푅푇 gas in the cylinder is Solving for , we find:푛 퐽 푚표푙 퐾 퐾 raised, the pressure will go up in proportion. 푛 = 0.156 It’s this pressure that pushes the piston. Heat engines run most vehicles in the world, and the So an empty gallon푛 jug sitting푚표푙푒푠 somewhere on Ideal Gas Law tells us why. the Earth’s surface contains this many moles of air. Recall that one mole is = 6.022 × 10 The Ideal Gas Law is also one of 4 equations of particles, and so the number of gas particles in23 gas physics that are combined to model the 푁퐴 the gallon jug is: structure of the Sun and other stars. These mathematical models afforded 19th century = physicists important knowledge about the Sun’s interior, long before much was known about = (0.156 푁)(6.022푛푁퐴 × 10 ) the nature of matter. 23 −1 푁 = 9.39푚표푙× 10 푚표푙 22 These are just a few of the many applications of Other Implications푁 of the 푔푎푠Ideal푝푎푟푡푖푐푙푒푠 Gas Law the laws of gas physics. The Ideal Gas Law is good for more than just counting gas particles. It tells us plenty about the behavior of gases. For example, a car engine is a type of engine called a heat engine, meaning that heat energy is transformed into kinetic energy. Each piston in the engine fits tightly inside its own cylinder. A mixture of gasoline and air are drawn inside the empty space above the piston. .
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