Ch 22: The Second Law of ThermodynamicsWorksheetSee all chapters
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Ch 01: Intro to Physics; Units
Ch 02: 1D Motion / Kinematics
Ch 03: Vectors
Ch 04: 2D Motion (Projectile Motion)
Ch 05: Intro to Forces (Dynamics)
Ch 06: Friction, Inclines, Systems
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Ch 22: The Second Law of Thermodynamics
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Ch 39: Quantum Mechanics

Concept #1: Introduction to Heat Engines


Hey guys, in this video we're going to start talking about heat engines. Heat engines are the most important application of the first law of thermodynamics and it's our first true application of the first law. Alright let's get to it. Now the first law of thermodynamics can be interpreted in many ways. One interpretation that we've used a lot so far is that heat transfer can change internal energy. Heat can lead to a change of internal energy which can lead to a change in temperature. This was very common in calorimetry problems. Another interpretation that we saw a lot when talking about thermal processes is that work can change the internal energy as well. Work can cause a change internal energy, that change internal energy can lead to a change in temperature or it can lead to heat being produced or a bunch of other things. Now something that we talked about before which is a the third interpretation of the first law of thermodynamics is important with regards to heat engines. So I want to refresh our memories of this. Now consider a gas contained in a cylinder that has a movable piston like shown, the cylinder does not have any thermal insulation. So we added heat into the gas here if the gases heated up, this gas is going to increase the average kinetic energy per particle. That's going to cause an increase in the average kinetic energy per particle. That's going to lead to a pressure increase, so the pressure increases. Now if the pressure increases, the force on the piston also increases. That increase in the force leads to a net force being placed on the piston and allows the piston to move. Now the pressure of the gas is strong enough to move against atmospheric pressure outside because don't forget that there is a gas in here at atmospheric pressure. Now the piston was initially here, it moved upward some delta X due to some force that force across the distance that means that work is being done. The net force causes the piston to rise, work is being done. This is the first example of a heat engine that we have. A heat engine is always going to be a machine that converts heat into usable work. What we've seen before as I said is heat being converted into internal energy which is converted into a temperature change and that can also go on in this scenario. I'm not saying that the temperature is constant of the gas in the piston but I am saying that not all of the heat goes into change in the internal energy, some of the heat also goes into producing work. We've talked a lot about this before in calorimetry and alike, now we're starting to talk about this process converting heat into usable work and that's the process in a heat engine. Now you could imagine the piston moving was attached to some other system so it could transfer the mechanical energy to another system to another system to another system to eventually accomplish something. This is the basis for how a car's combustion engine works. Pistons are moving up and down inside of a combustion engine and they deliver energy by being connected directly to the crank shaft. The piston is oscillatory motion, the piston's moving up and down, and that converts the energy, delivers energy to the crank shaft and converts it to rotational energy in the crank shaft. The crankshaft eventually connects to the drive shaft, the drive shaft eventually connects to the wheels which is where you want the energy to go. You want the energy to go from the piston all the way to the wheels and that is how a combustion engine drives the car. Now a heat engine has three important components that you have to know. It has a hot reservoir which I've shown here, TH is the temperature of that hot reservoir, it has a cold reservoir which I've shown here, TC is the temperature of the cold reservoir and it has the actual engine itself, whatever is actual machine that allows the system to undergo the process that converts heat into usable work and the engine is typically represented by a circle that might say engine inside of it, I'm just going to draw a capital E so that we know what's happening.

Now what's going on in a heat engine is we have some heat leaving the hot reservoir which I called QH. That heat enters the engine and the engine churns and splits it up into usable work and heat that returns to the cold reservoir. The energy powering the engines is the heat flow from the hot reservoir to the cold reservoir so there's a net heat flow from the hot to the cold reservoir. As heat flows from hot to the cold, the engine converts some into work. Right here we have an equation that the hot, sorry, the heat from the hot reservoir has to equal the heat to the cold reservoir plus W where all of these are positive numbers, all these are magnitudes. So given the fact that some heat returns to the cold reservoir W has to be less than the heat from the hot reservoir. So the engine can convert some of this heat that flows from the hot reservoir to the cold reservoir, it can convert some into work. An engine absolutely 100 percent cannot convert all heat into work. Some of the heat must go in. This heat right here must not be zero. If it were to be zero that would violate the second law of thermodynamics which is something that we're going to cover in a lot more depth later on but for now you can just take that on faith that no engine could ever convert one hundred percent of the heat from the hot reservoir into work, some has to be left over to be sent back to the cold reservoir otherwise it would violate the second law of thermodynamics. So an example, an engine compressed gas at a constant pressure. If at atmospheric pressure the engine requires an input of 500 joules to compress the gas from some volume to some smaller volume, how much heat is transferred to the cold reservoir? So remember our engine diagram. We have some hot heat, some heat from the hot reservoir coming in, we have work coming out and we have heat returning to the cold reservoir. This tells us that the heat from the hot reservoir has to equal the heat returning to the coal reservoir plus the work where all of these are magnitudes no signs here, all positive numbers. Now since this is at constant pressure, we know that the work is negative P delta V so we can find the work easily, -P delta V. This is occurring at atmospheric pressure which is 1 times 10 to the 5 Pascals, the change in volume we are given 0.0005 minus the initial volume 0.001 and this equals 50 joules being done. So that's the work being done. If the engine requires an input, the input is the amount of heat from the hot reservoir, of 500 joules. So we know Q hot is 500 joules. This means Q cold, the amount of heat transfer to the cold reservoir is going to be Q hot minus W which is going to be 500 joules minus 50. Everything is positive signs here, all we're dealing with are magnitudes and this equals 450 joules. So that's how much heat is transferred from the engine to the cold reservoir. So out of all of the initial heat that we're given, only one 9th sorry one 10th of it, 50 joules, one 10th of it 10 percent of it is converted into work. Only 10 percent is converted into work, the other 90 percent goes back to the cold reservoir. Alright guys that wraps up our introduction to heat engines. Thanks for watching.

Practice: A proposed engine has three steps: one step that does 30 J of work ON the gas, one step that does no work, and one step that does 50 J of work BY the gas. Is this an example of an engine? If so, what is the minimum heat input required?