 Hello, my name is Adrian and welcome to another video of understanding thermodynamics, where today we are going to discuss the ideal gas law, where we combine several properties into one equation. So the contents of this video will include the concept of the ideal gas, the ideal gas law itself, degrees of freedom of the ideal gas, and then lastly, we will discuss absolute temperature. The kinetic theory of gases consider a gas as a collection of particles that collide elastically with each other and with the walls of a container and do not attract or repulse each other. So there's no forces between them. You can think of them like billet balls on the table. And we also assume that the particle is what is called a point particle. So their volume is negligible or even zero. So we don't we don't think about the volume at all. And such a gas is called an ideal gas. And this gas obeys the ideal gas law. The ideal gas law is a theoretical concept. In other words, an ideal law does not exist. However, when the temperature of a gas is high, the kinetic energy of an individual particle is much higher than energy associated with inter particle traction or repulsive forces that do exist in real gases. And when the specific volume is also high, so the density is really low, the particles on average far away from each other, which reduce the inter particle forces. So they don't really collide with each other. Also, the total volume of the gas particles is much less than the volume of the container itself. We can therefore assume the ideal gas law behavior for gases at high temperatures and low pressure. But then this begs the question, how high is high for nitrogen, which boils at minus 196 degrees 20 degrees is is high. But then when we look at water, water is still liquid at 20 degrees Celsius. So for water 20 degrees is not really that high temperature. Now, as a rule of thumb, we can assume ideal gas behavior as long as the pressure at which this gas is is less than one third of the gases critical pressure. And the temperature is at least twice the gases critical temperature in everyday use, oxygen and nitrogen meets this high temperature and no pressure criteria. And we usually assume that air is an ideal gas and therefore based the ideal gas law as well, at very, very low pressures, less than 0.01 times the critical pressure, it is generally safe to assume ideal gas behavior at all temperatures. So then we can sort of neglect the temperature rule that needs to be twice the critical temperature. So this brings us to the ideal gas law, which is pv equals nr dash t. Now this equation is valid for any gas. In engineering, we prefer to use kilograms rather than moles or kilomoles, and therefore we manipulate the ideal gas law. And the following steps just show you how we convert the initial ideal gas law to one that we will use in an example on the next slide. We can calculate the gas constant r for a specific gas and rewrite the ideal gas law, where pv is equal to the mass multiplied by a gas constant and t. But now this r has a unique value to the specific gas that we're looking at. So let's do an example of this new equation. So we need to calculate the mass of one cubic meter of nitrogen at 25 degrees Celsius and 100 kPa. Now the first thing we do is we calculate the gas constant that will be specific to nitrogen. You can see we use this equation over here where the gas constant for nitrogen is in fact the universal gas constant divided by the molecular mass of nitrogen. Then once we've got that, we can now go and use our modified ideal gas law to calculate the mass of the nitrogen inside this cubic meter container. And we get an answer of 1.13 kilograms of nitrogen. Just a few things to note, because we have denoted 25.0 degrees Celsius, which is three significant figures, we also report the kilogram in three significant figures. And when we say pressure, in this case p, we refer by default to the total pressure. We've calculated the gas constant for nitrogen, but you are able to find these values in tables in your handbook as well. We can also go and rewrite the ideal gas law to contain only intensive variables by making use of the equation for specific volume. Now specific volume is equal to the total volume divided by the mass of the gas. And then the ideal gas law then becomes pressure times specific volume equals gas constant times temperature. Next let's look at degrees of freedom. Now the temperature and pressure of air in an open container, for instance the room of a house are independent of each other. We can heat up the air in a room without the pressure changing. And in an ordinary house, the pressure of the air inside the house is determined by the ambient temperature outside. Now when we know the values of temperature and pressure of this air in the room, we can then use the ideal gas law to calculate the specific volume. In actual fact, we can now calculate the value of all other intensive properties of the air such as density and viscosity. We will encounter and calculate the value of other intensive properties such as internal energy, enthalpy and entropy later. We can therefore say that once the value of two independent intensive variables are fixed, the state of the substance is fixed as well. This is true for all single phase simple substances. Once the value of two independent properties are fixed, the state of that substance is fixed as well. We can therefore say that system has two degrees of freedom. Just a note, a simple substance is one that is free of magnetic, electrical and surface effects. Lastly, let's look at absolute temperature. Now conditions where we can assume ideal gas behavior, we can plot the value of pressure against temperature for three different gases A, B and C. Now at constant volume, when we change the temperature, we will get dots which will create a straight line which will intersect the x-axis at minus 273.15. And this will be the case for any ideal gas. The pressure cannot go lower than zero and this intersect also represents the lowest value of temperature and enable us to calculate an absolute value for temperature. Now let's summarize. For gases at very high temperature and low pressure, we can use the ideal gas law. The ideal gas law is pressure times specific volume equals gas constant times temperature. Each substance has its own value for R, which is our gas constant. For single phase simple substances, there's only a two degree of freedom for that system. And once two intensive variables are fixed, the whole system is fixed as well. And lastly, we have demonstrated the existence of absolute temperature. Thank you very much for watching the course notes, which these videos are based on, is available on my website, www.odderonsblog.com. You're also welcome to connect with me on Twitter. My Twitter handle is at SVN90, where if you've got any questions, you're welcome to ask them and I will answer them accordingly. Thank you very much for watching and I will see you in the next video. Bye.