Question

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

Answer 1

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 ..

Answer 2

I know slope = 0 corresponds to the phase change

Answer 3

yes, what do you think?

Answer 4

the slope is steeper for the solid

Answer 5

I think the heat of fusion is easy to see from the graph :
2 is greatest and 1 is smallest

Answer 6

Oh right right, we could compare the slopes !

Answer 7

Yeah, if it is steep, then it's easier to change its temperature so it has a very low capacity.

Answer 8

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

Answer 9

Yes, way to go.

Does your book cover Newton's Law of Cooling?

Answer 10

Nope. It does have below equation on conduction rate :
\[P_{cond} =kA\dfrac{\Delta T}{L} \]

where \(k\) is conductivity of the material

Answer 11

Ah, these are very fun. I'm going to give you a few nice questions on this. :)

Answer 12

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

Answer 13

Indeed these are really fun :) let me finish other parts..

Answer 14

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

Answer 15

, (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

Answer 16

(d) specific heat in the solid state

this looks a bit tricky... how to interpret the graph 3 ?

Answer 17

This is \(C=0\).

Answer 18

Ahh okay, then \(1\) has greatest specific heat and \(3\) has lowest(0)