![]() ![]() PV diagram, that state variable should be that value. Say, U, which is internal energy, at any point in this General idea that in order to have a state variable like, ![]() Furthermore you have to add 10 j to 2w because you start from state A. Morover you have to add to this value 10J, because it's the heat content in your system at state A: in fact if you keep going around the carnot cycle and eventually you return at state A, the value of your heat content won't be equal to 10J + w, but 10J + 2w, because Q is equal to 2w and in fact you have to add a value of heat equal to the energy transferred thanks to the work to keep the temperature constant, avoiding its reduction( because it is an isothermic process > and so I have to replace the energy which i take away from the system thanks to work, adding the same value of heat). Heat, in the video, is equal to work because the internal energy of your system doesn't change, so the net heat is equal to the work done by the system. Ok, now, also if I'm not sure of my answer, I'm going to answer your second question. ![]() Instead what you spend in terms of heat it's different, because you follow two different paths ( the elevator or the staircase). The height between the floor two and one is a state variable, so we don't care about how do we get to the second floor ( the path), because the height between these two floors is the same. So it dipends on the path, think about this example: you have two ways to get to the floor one to the floor two, the elevator or the staircase. So you are able to find the value of heat only if you have transition of energy. But the amount of W or Q needed depends heavily on what path you took to that PV point (iso-volume is no work, etc).īecause Heat isn't an intrinsic property of the system, therefore you are not able to evaluate the heat without talking of exchange of energy with the enviroment, In fact it's a measure of the flux of energy. Likewise P, V, T, S, and U are always the same at the same point on a PV diagram, no matter what wacky path gets you to that point. Is your elevation a state variable for a mountain top? Yes. If you crawled up the mountain, you would be more tired than the person next to you who parachuted in. Is "tiredness" or "effort" a variable that is always the same for someone on top of the mountain? No. Those coordinates DEFINE your location on the mountain top. Think if it this way: On a mountain top, there are always the same Latitude and Longitude, not matter if you hike straight up, or cycle around the mountain, or parachute in. So if you choose P1 and V1 as your point for a certain system of ideal gas, no matter how you change P and V, when you get back to P1 and V1, the U will be the same as it was at the beginning (U1). There are a lot of other posts on this site worth consulting for more on similar questions.A state variable means it will always be the same AT THAT POINT. That the above relation between heat, T, and entropy exists is remarkable (and has other implications, for instance wrt the definition of heat and T), but it is essential to remember that in general entropy is a property of the states, not of the path. The entropy is a property of the system, not of the path. The rather remarkable thing is that there is a special (and ideal) way of transforming one system into another that will provide the magnitude of the entropy change for any transformation, and that is to sum the ratio of the heat produced to the temperature at each of infinitely many infinitely small steps of a reversible path, one performed infinitely slowly: $$\Delta S = \int_1^2 \frac$$Īlthough this is presented as the definition of the entropy (according to one formulation of the 2nd law), it is a thermodynamic definition and can lead one to miss the forest for the trees. Since the change only depends on the states of the end points, if you find some way of determining the entropy difference, say by performing a transformation in a particular special way, then that difference must be the same for all possible processes that take you between the two states. Since the entropy is a state variable, the difference in entropy must also be constant for two specific states. Entropy is a state function because it depends only on the arrangement (as a statistical average) of the constituents of the system at the given values of the thermodynamic variables (T,P,V etc), not how the arrangement was obtained. You could regard path independence as the defining property of a state function. The fact that entropy is a state function is what renders it path-independent. ![]()
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