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# More on entropy

Distinguishing between microstates and macro states. How entropy S is defined for a system and not for a specific microstate. Created by Sal Khan.

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• I'm confused. If there are an infinite ammount of points in a 3 dimensional space, then can't a molecule occupy an infinite ammount of different states? (orientation, position, etc.) So even if you increase the volume, it's still and infinite ammount of states right? Or am I just misunderstanding the use of the word 'state'? • Can someone explain to me why elements in their standard states do not have 0 entropy? (i.e. S = 0)
Thank you • One definition of entropy I have read is "a measure of the energy that is no longer available to perform useful work within the current environment", but it seems much different from the definition given here. Can someone help me make the connection between the two definitions? • Suppose you have a gas that is expanding and moving a piston from left to right, thus doing "useful", i.e. mechanical, work. Since the gas particles are transferring a net rightward momentum to the piston, there is a net rightward velocity to the particles. There are not as many ways to get this state as there are to get a state where the particles are moving completely randomly. The piston eventually stops moving because the excess rightward momentum of the particles has all been transferred to the piston and now the particles are moving completely randomly, and the entropy of the gas is higher. Then no more useful work is possible. The particles are still moving and still have kinetic energy, but there's no way to capture it to do mechanical work.
• If heat is added to an ideal gas (+q) how much of that heat will be converted to mechanical work (-w)? Given that entropy is "a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work" would it be as simple as dividing the heat put into the system (+q) by the temperature of the system (T) Q/T=S and deducting that S value from the heat put into the system (+q) to find the total amount of energy left to do mechanical work? If U = Q - W and 10 J of heat is added to the system, is the change in internal energy (U), which is the amount of energy not lost to work after the heat was added, equal to entropy's negative affect on converting that heat put into the system into mechanical work (-S)? • but then why do we associate entropy with disorder ?? how does a disordered system take on more states ?? • Can someone give me a super quick and easy definition of entropy?
(1 vote) • so only system has entropy and state does't has right? I mean if the state dissipates some heat then there would be entropy right? • If the larger box had all 8 particles in one corner, would that change anything in relation to whether one can call it more/less entrophic than the small box? I realise that they're both micro states, and it doesn't tell you much about the system, but for that minuscule moment, would it change anything?
(1 vote) • The entropy is determined by the number of possible states, not by the particular state at one moment. 8 in one corner is just one of many many possible states, and we would expect that state to have as much likelihood as any other, so there's nothing special about it that would make you change your view of the entropy. If the particles were constrained to one corner, that would be a different story  