ganeshie8
  • ganeshie8
Three different materials of identical mass are placed one at a time in a special freezer that can extract energy from a material at a certain constant rate. During the cooling process, each material begins in the liquid state and ends in the solid state; Fig. 18-26 shows the temperature T versus time t. (a) For material 1, is the specific heat for the liquid state greater than or less than that for the solid state? Rank the materials according to (b) freezing-point temperature, (c) specific heat in the liquid state, (d) specific heat in the solid state, and (e) heat of fusion, all greatest first
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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dakid88
  • dakid88
only on the material's state (temperature, pressure, and volume). .... The heat of vaporization LV is the amount of energy per unit mass ... 4 A sample A of liquid water and a sample B of ice, of identical mass ... time in a special freezer that can ex- ... each material begins in the liquid state and ends in the solid state; Fig. 18-27 ..
ganeshie8
  • ganeshie8
|dw:1450359424508:dw|
ganeshie8
  • ganeshie8
I know slope = 0 corresponds to the phase change

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ParthKohli
  • ParthKohli
yes, what do you think?
UnkleRhaukus
  • UnkleRhaukus
the slope is steeper for the solid
ganeshie8
  • ganeshie8
I think the heat of fusion is easy to see from the graph : 2 is greatest and 1 is smallest
ganeshie8
  • ganeshie8
Oh right right, we could compare the slopes !
ParthKohli
  • ParthKohli
Yeah, if it is steep, then it's easier to change its temperature so it has a very low capacity.
ganeshie8
  • ganeshie8
a) For material 1, is the specific heat for the liquid state greater than or less than that for the solid state? since the slope during liquid state is less steep, the specific heat for the liquid state must be greater
ParthKohli
  • ParthKohli
Yes, way to go. Does your book cover Newton's Law of Cooling?
ganeshie8
  • ganeshie8
Nope. It does have below equation on conduction rate : \[P_{cond} =kA\dfrac{\Delta T}{L} \] where \(k\) is conductivity of the material
ParthKohli
  • ParthKohli
Ah, these are very fun. I'm going to give you a few nice questions on this. :)
ganeshie8
  • ganeshie8
Nope. It does have below equation on conduction rate : \[P_{cond} =kA\dfrac{\Delta T}{L} \] where \(k\) is conductivity of the material \(L\) is thickness \(A\) is crossectional area
ganeshie8
  • ganeshie8
Indeed these are really fun :) let me finish other parts..
ganeshie8
  • ganeshie8
Rank the materials according to (b) freezing-point temperature, During a phase change, the temperature doesn't change. From the graph, its easy to see \(1\) has greatest freezing point and \(3\) has lowest
ganeshie8
  • ganeshie8
, (c) specific heat in the liquid state, again, comparing slopes in liquid state we see that \(1\) has slowest change, therefore its specific must be greatest : 1, 3, 2
ganeshie8
  • ganeshie8
(d) specific heat in the solid state this looks a bit tricky... how to interpret the graph 3 ? |dw:1450360409654:dw|
ParthKohli
  • ParthKohli
This is \(C=0\).
ganeshie8
  • ganeshie8
Ahh okay, then \(1\) has greatest specific heat and \(3\) has lowest(0)
UnkleRhaukus
  • UnkleRhaukus
|dw:1450360591255:dw|
ParthKohli
  • ParthKohli
The other extreme is \(C=\infty\). That's the heat capacity of boiling water.
ganeshie8
  • ganeshie8
I believe so... all temperatures must be same once the system reaches steady state
ganeshie8
  • ganeshie8
In liquids mercury has lowest specific heat water has largest
ganeshie8
  • ganeshie8
or do you mean the temperature of water doesn't change during vaporization ?
ParthKohli
  • ParthKohli
Yeah, just look at phase change graphs.
ganeshie8
  • ganeshie8
therefore we can "think" of the specific heat of boiling water as \(\infty\) something ?
ganeshie8
  • ganeshie8
but that kind of interpretation doesn't look correct to me
ParthKohli
  • ParthKohli
At phase change, a lot of heat is absorbed and no change in temperature occurs, right?
ganeshie8
  • ganeshie8
we should not treat the phase change event as another phase of water...
ganeshie8
  • ganeshie8
the energy is used up to break the bonds etc, but this doesn't mean the specific heat of boiling water is infinity
ganeshie8
  • ganeshie8
or does it ?
ganeshie8
  • ganeshie8
i don't know ..
ParthKohli
  • ParthKohli
well, all specific heat cares about is if I take a unit amount of some substance and supply differential amount of heat, what's the differential change in temperature? if it doesn't change, then at that particular state, its heat capacity is infinite.
ganeshie8
  • ganeshie8
the concept of specific heat makes sense only when the matter is not changing its phase when the matter is changing its phase, we use heat of vaporization/fusion right ?
ganeshie8
  • ganeshie8
Based on your interpretation, you could argue that the specific heat of any matter during a phase change is infinity... what good is this interpretation ?
ParthKohli
  • ParthKohli
yes, there's not much you can do, but it has to be infinity. and we can appreciate that fact.
UnkleRhaukus
  • UnkleRhaukus
hmm, it's not even an exaggeration.
ganeshie8
  • ganeshie8
I see... even the definition of specific heat has nothing to do with phase change, so this infinity business should be okay i guess..
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