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At room temperature, when you place an ice cube (the system) on the table in front of you; which expressions are correct as it melts?ASsys <0 and ASsurr < 0AS...

Question

At room temperature, when you place an ice cube (the system) on the table in front of you; which expressions are correct as it melts?ASsys <0 and ASsurr < 0ASsys >0 and ASsurr > 0ASsys <0 and ASsurr >0ASsys >0 and ASsurr < 0

At room temperature, when you place an ice cube (the system) on the table in front of you; which expressions are correct as it melts? ASsys <0 and ASsurr < 0 ASsys >0 and ASsurr > 0 ASsys <0 and ASsurr >0 ASsys >0 and ASsurr < 0



Answers

In which quadrants are the statements true and why? $\cos x<0$ and $\sec x>0$

So we're taking a look at an ice cube and we'd like to know. Are there any conditions such that an ice cube can melt? Reversible? E and there is one condition at which you can melt reverse obliquely. And when you want to think about a reversible process, you should really be thinking equilibrium. And so if we're thinking about equilibrium of melting of an ice cube, well what is really going on there? Right. We have a combination of melting and freezing and what conditions could we have? Where if we just add a little bit of heat we can melt. But if we remove some heat we can freeze and at normal conditions at one atmosphere of pressure we can do that At 0°C and 0°C.. If we add heat we will melt. If we remove heat we will freeze. We have an equilibrium between the solid and the liquid. So where we have a phase change, we can have irreversible process. Now if this ice cube does melt reversible, e what does that tell us about the change in energy of the system? Is it zero? Or is it non zero? And No, it won't be zero. And how do we know that? Well, we know that? Because when we do melt, when we break the I. M. F. C. To take a solid and make it a liquid, we know that we add energy to our system in order to do that. So, melting overall increases the energy of a system. And thus, if that's true, the change in energy is not equal 20

Okay. What we want to do is we want to look at four statements and determine which one or ones are equivalent to the plant delta definition of a limit. So the first thing, let's go ahead and write down that epsilon delta definition um and say let's say that um the limit as X approaches c of f of X equals L means that for each epsilon greater than zero, there is a corresponding yeah mhm delta greater than zero. Such that absolute value of F of x minus L is less than epsilon. Provided that zero is less than absolute value X minus c. Less than delta. Or we can say that zero less than the absolute value of x minus C, less than delta implies that the absolute value of F of x minus L is less than epsilon. Okay, so let's kind of look at these four statements. Um I would say a is not an equivalent statement because even though it says for some epsilon and every, the key thing is that every delta greater than zero. Right? Um For the excellent delta definition is that for each epsilon greater than zero there is a corresponding delta greater than zero, Right? So it's not for some random, Excellent, greater than zero. And every delta it's the epsilon and the delta have to correspond to each other. So is off the table. Um Now let's say for every delta greater zero there is a corresponding epsilon. So those are kind of a mismatch orders. But you notice that um they switch the delta and epsilon role. Um And so it could be the delta excellent definition. Right? And not the epsilon delta definition, it could be the delta epsilon. So here you notice that for each epsilon greater than zero there is a corresponding delta. So delta went went with the x minus c, and epsilon went with the function, but in this case they just kind of changed the roles. So I would almost say this is equivalent. So one of the key things is we have to remember not to get so absorbed um or focused on notation that we can interchange notation and keep the same meaning. Okay, so see for every positive energy and there is a corresponding positive energy am such that um and notice the role of one of M and M as long as I do the same thing, one over M and one over in. So I would only say that this is also equivalent and then for every epsilon greater than zero there is a corresponding delta. Such that. Um And um so here the this is the conundrum. So the end um this statement implies the validity of the function statement. So this conjunction word of an means that those who have to occur. Um This occurrence implies that this will be true, not that they, and for some reason, so I would almost take off D and I would always say BNC hope this helped.

So we want to know where will the sine of an angle be positive and the cozy can't of that same angle B. Negative? And the answer to that question is that's never going to take place because the sign and the corsican are reciprocal functions. This is the y coordinate on the unit circle, and this is one over the Y coordinate on the unit circle, and they're always going to have the same s i g N. Sign.

In this problem I'm gonna take a look at the inequality zero is less than the absolute value of X -8 which is less than D. So what this means, I'm gonna start with the absolute value of X -8 is greater than zero. This means that the distance between X and eight is greater than zero, so X. Is not allowed to equal eight. And on the other side of this, absolute value of X -8 is less than D. That means that the distance between X and eight is less than whatever number D. Is. So we actually build our solution off of the right side of this, we say negative D. Is less than x minus eight which is less than D. And then we just solve this inequality. There's only so much we can do because we don't know the value of D. But we can kind of see what's happening overall. So whenever I grab this I'm going to have- D. Plus eight and positive D. Plus eight and then eight is in the middle and eight cannot be part of our solution. So there's a circle around it and our other two in points are also circles and everything else is in the middle that is bolted for X. So this is negative D. Plus eight 28 and pick that back up at eight two d. Plus eight. But the actual value of eight is not included.


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