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This video covers "work" -- this is a specific category of energy concerned with pushing against a force, or expanding against pressure.
The previous lecture talked about total  energy, and then heat transfer. Heat is the   microscopic transfer of kinetic and potential  energy by collisions. And heat transfer can   happen where a system meets its surroundings. Now, we’re going to look at another aspect of   thermodynamic interactions , work. This is a  measure of energy and energy transfer that is   distinct from the transfer of heat. we already know that there is an   internal energy. We’re going to label that ‘U’, to  help differentiate it from just a generic energy.   This is the sum of kinetic and potential energy  inside the system.
So, if we picked up our sample   and moved it around, or raised it up against  gravity, the internal energy wouldn’t change.  Make sure you’re happy with that  definition of internal energy.   It’s always with respect to a system, and it’s  important to understand the scope of the system. 
Any change in the system’s state is accounted  for by an internal energy change. And, mostly,   we’re dealing with closed systems, so this change  is just heat flowing in and out of the system.  Now we’re going to move onto work. To study work we usually think about   pistons. All very 19th century, but it’s  quite easy to justify the maths this way,   and then start worrying about other setups later. More generally, though, we’re thinking   about how a system can interact with its  surroundings by expanding or contracting.  A cylinder like this will have a pressure  bearing down on it, compressing the gas   inside. And that pressure produces a force.
Which  we can calculate using the area of the piston.  Don’t worry about what the area is, because  it’s going to become irrelevant shortly.  The gas inside also has a pressure, pushing  up on the area of that piston, and therefore   exerts a force. And when they’re in balance,  there’s no movement, and no exchange of energy   occurs except for heat on the microscopic level. If we increased the pressure outside   then that piston would be compressed by the  increase in force. The lid would move over a   distance. And pushing against a force over  a distance gets us energy . In this case,   we refer to the energy expended here as  “work”.
Any movement against a force is work.  Now we can look at why that area  wasn’t really necessary to worry about,   because we can substitute that force  for just the pressure and the area.  And what is that area times that distance?  It’s a volume. Specifically, the change   of volume of the gas. So, it doesn’t matter  if this is a piston, or a balloon, or even a   packet of air that’s just floating around, the  work done is proportional to the volume change. 
Keep an eye on the negative sign, though. If the change of volume is positive,   meaning it’s expanded, then the work is negative . This means that energy has been transferred out of   the system. The internal energy has reduced. If the change of volume is negative,   meaning it’s compressed, then work is  positive work and energy has been added   to the system. The internal energy has increased. Providing no other heat has been transferred,   that’s the one we labelled q and talked  about in the last lecture, then the change   in internal energy is equal to the work done. This leads to something that should be obvious   if you’ve followed so far.
The change in internal  energy, Delta U, is equal to the work done plus   the heat transferred. This simple expression,  here, is the first law of thermodynamics.  We know energy cannot be created  or destroyed, just moved around,   and this is what the equation is saying. A system has an internal energy,   any change to it is fully accounted for by the  heat transferring in and out of it, that is,   the microscopic collisions, and  the work done to and by the system,   which is a more macroscopic view of energy. So in this simple statement is a founding   principle of physics and the universe,  that of conservation of energy.

Here, we begin to relate energy and pressure together.

Energy and pressure

Pressure multiplied by volume is energy. You can see this from the ideal gas law, where pV = nRT leads to energy on both sides. So a change in pressure and volume must relate to an energy change. Providing pressure is constant, we can define a specific type of energy known as work, w.

[-pDelta V=w]

This is probably one of the stronger definitions of what energy is: energy is a quantity that can cause work to happen.

This is because changing a volume against an external pressure requires pushing against a force over a particular distance. This can either be thought of as multiplying the force by the distance moved, or integrating it over the distance if the force is not necessarily constant. Therefore force is a derivative of energy. Specifically, here, potential energy because these changes alter the configuration of the system.

[V=-int F:dx] [F=frac{dV}{dx}]

For the purpose of this course, we won’t be looking at integration and differentiation, but if you’re already aware of it, this is what is happening more precisely.

Signs – positive and negative

It’s worth noting the sign of these values – the relationship is between work and the pressure/volume change is defined as negative. This is because expansion takes energy from the system, so its energy must become lower.

Relationship to internal energy

Work done will alter the internal energy, U, of a system by changing its configuration. A system’s internal energy may also be altered by heat. Heat is the transfer of energy by microscopic collisions. Any internal energy change must be accounted for by work and heat.

This leads to the first law of thermodynamics, which is mostly a statement about conservation of energy.

[Delta U = w + q]

Note the sign here. Adding these two quantities is the convention within chemistry. You may see it written differently in other disciplines, which define the direction of heat flow and work differently depending on their needs.

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Introduction to Thermodynamics

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