[BLANK_AUDIO]. In this video, I shall present the first law of thermodynamics, and show how it governs the state function internal energy, and how considerations of the first law for isochoric and isobaric processes leads to the definition of the further state function called enthalpy. Around 1850 the German scientist, Rudolph Clausius, took the law of conservation of energy, which states that energy can neither be created nor destroyed, merely changed from one form into another, and applied it to the idea of a thermodynamic system. All matter possesses internal energy, symbol U and thus, so do all thermodynamics systems. We as human beings have a very intimate relationship with our own internal energy. As we live our everyday lives, we constantly release energy into our surroundings by a radiation of body heat, performing mechanical work going to movement, and even through sound waves when we speak. As a result, our internal energy is constantly decreasing. We boost our internal energy by keeping ourselves warm through heating systems and by consuming food. If our internal energy begins to fall to dangerously low values, our body responds by sending signals to the brain, causing for example, shivering, stomach ache, and headaches. Measuring absolute internal energy is virtually impossible, owing to the complexity of matter. And so it's more normal for us to consider changes in internal energy, delta U. What Clausius realized, was given energy can neither be created nor destroyed, any energy that enters or leaves a thermodynamic system must result in a change in the internal energy of that system. This is expressed in mathematical form using the conventions laid out in the second lecture as equation one. Delta U equals q in plus w on. The heat supplied to, plus the work done, on a thermodynamic system, must result in a change in the internal energy of that system. Q in, and w on, are positive for energy entering the system and result in an increase in internal energy. Whereas q in and w on are negative for energy leaving the system and result in a decrease in the internal energy. As a side note, all the really important equations in this course will be boxed and highlighted in a similar fashion to equation one. So thinking in terms of chemistry, it is usually obvious when a reaction releases heat energy. But how might a chemical reaction perform mechanical work? The answer is when a gas is released. The reaction between zinc metal and hydrochloric acid produces hydrogen gas, as shown in the equation on the slide. The gas is released into the solution in the form of bubbles, which then rise to the surface and burst. Hydrogen molecules are thus released into the atmosphere whereby they collide with nitrogen and oxygen molecules, effectively pushing the atmosphere back. This process is clearly invisible, however the emerging gas does perform mechanical work in pushing the atmosphere away. To quantify the work done, imagine a gas stored in a cylinder with a frictionless, massless piston of cross sectional area A. Now imagine the gas expands pushing the piston through a distance d, against an external pressure p. The work done by the gas is the force exerted on the piston multiplied by the distance through which the piston moves. The pressure on the piston is defined as the force exerted on the piston, divided by its cross-sectional area. And thus, the force exerted on the piston is equal to the pressure on the piston, multiplied by its cross-sectional area. If we now substitute this expression for the force exerted on the piston into the expression for the work done by the gas, we find that the work done by the gas is equal to the pressure, multiplied by the cross section area of the piston, multiplied by the distance through which the piston moves. But the cross-sectional area of the piston, multiplied by the distance through which the piston moves, is equal to the change in volume of the gas delta V. So, the work done by the expanding gas is equal to the pressure multiplied by the change in volume of the gas. Hopefully this intuitively makes sense. The greater the volume of gas released, the more work needs to be done to push the atmosphere away. And the greater the pressure, the more work needs to be done as it is harder to push the atmosphere away. Finally when a gas is released by a chemical reaction, work is being done by the thermodynamic system. And so by convention, the work done on the system is negative. And thus w on equals minus p delta V. This is a very important result, and we shall denote it equation two. If we now revisit the first law of thermodynamics, delta U equals q in plus w on, as we have just shown, w on is equal to minus p delta V. Thus, the first law becomes delta U equals q in minus p delta V. Expansion work therefore depends on pressure and change in volume. There are thus two ways to make the expansion work zero. The first way to make expansion more equal to zero is to perform the reaction under conditions of zero pressure. When p equals zero, minus p delta V equals zero. No expansion work is done, because the gases expanding into a vacuum. And thus the first law of thermodynamics becomes simply delta u equals q in. The change in the internal energy of a system is equal simply to the heat supplied to the system. This is called free expansion. However, given the number of human beings that have ever been into space, relatively very few experiments are carried out under such conditions. The second way to make expansion work equal to zero is to perform the reaction at constant volume. On the isochoric conditions, delta V must be zero and this minus p delta V equals zero. No expansion work can be done, because any gas produced simply cannot expand. Under these conditions, the first law of thermodynamics simply becomes delta U equals qv. The subscript v denotes the heat supplied q in at constant volume. This equation is important and is given as equation three. The major consequence of performing reactions at constant volume is the risk of serious pressure change. Consequently, constant volume reactors are invariably made of thick stainless steel and have lids secured with massive metal bolts. Such engineering is extremely expensive. And consequently isochoric processes are most often the domain of the heavy chemical industry and chemical engineering. Most chemists on the other hand perform chemical reactions in glassware under isobaric conditions. In this case, the first law of thermodynamics does not simplify. It was therefore necessary to create a new state function called enthalpy, symbol H. Enthalpy is defined as H equals U plus pV. And therefore the change in enthalpy, delta h, equals delta u plus delta pv. Since pV is a product, we must use the product rule to differentiate it. Thus, delta H equals delta u plus p delta V, plus V delta p. But, for an isobaric process, pressure remains constant, and therefore, delta p equals zero. Thus, the V delta p term disappears to give delta H equals delta u, plus p delta V. Now it should hopefully be apparent why enthalpy was defined in this specific way. Because delta u plus p delta V is the left hand side of the second equation on the slide. We can therefore substitute delta H for delta u plus p delta V. And the first law of thermodynamics at constant pressure becomes delta H equals qp. The subscript p denotes the heat supplied q in at constant pressure. This equation is very important and is given as equation four. So in summary, the first law of thermodynamics arises from the application of the law of conservation of energy to thermodynamic systems. The expansion work done by a gas is p delta V, but this is the system performing work, and so in the context of work performed on the system, this becomes minus p delta V. The heat supplied to a thermodynamic system at constant volume is equal to the internal energy change of the system, delta U. Well, so heat supplied to a thermodynamic system at constant pressure is equal to the enthalpy change of the system, delta H. The former is very much the domain of heavy industry and chemical engineers, whilst the latter is the domain of chemists. In the next lecture, we shall examine the important concepts of reversible expansion work. [BLANK_AUDIO]