Question

@Vincent-Lyon.Fr @Callisto
Find the temperature of the final mixture, assuming that:
1. The s.h.c. of ice between -15C and 0C is 2050J/kg/C
2. The s.h.c. of water is 4020J/kg/C
3. Specific \(L_f\) of ice is 3.34x10^5
Picture below:

Answer 1

Do you have any idea what you can do?

Answer 2

I would do the following but it's not correct:
0.2*4200*(25-T) = 0.1*2050*(0-(-15)) + 0.1*3.34*10^5 + 0.1*4200*(T-0)

Answer 3

There is so much ice, that you will probably reach a state where ice and water are in equilibrium at 0°C

Answer 4

how can i do it then?

Answer 5

0.2*4200*(25-0) = 0.1*2050*(0-(-15)) + m*3.34*10^5

where m is the mass of ice that will melt.

Answer 6

Sorry I do not follow, and how do you know whether it will be 0C, <0C or >0C in the beginning?

Answer 7

Your first attempt was legitimate.
What did you get for T when you solved it?

Answer 8

12

Answer 9

Really? So what is the problem?

Answer 10

The problem is that the book writes 0

Answer 11

So, the book must be correct.
I'll try to solve your equation: I bet you end up with a negative value for T.

Answer 12

sorry it's -12 my fault

Answer 13

@aidanwong asked me this question and i brought it here with you

Answer 14

Ok, so this proves that your first assumption (all ice melts and mixture in 100% liquid in the end) is false.

So final state is liq+solid , and temperature cannot be other than 0°C. Problem solved.

Answer 15

oh i see, but how do you know if the mixture isn't all solid?

Answer 16

It takes more heat to cool water by 1°C than to warm ice by 1°C.
SO final state cannot be all solid because there is more water than ice and water is higher above 0°C than ice is below °C.

Answer 17

oh i see, thank you

Answer 18

can you explain your equation to me? I don't understand why we need m

Answer 19

We don't. But the question could have asked for it.

Answer 20

Oh I see, I finally get it now.
(My mind at 01:24 ain't perfect)

Answer 21

Good night ! Here is 18.25 only.

Answer 22

The earth is round :)

(@aidanwong is back again?)

Answer 23

@aidanwong oh my god lots of evidence show that my mind is not functioning now, sorry bye

Answer 24

thanks for helping...
actually freezing the water requires so much energy that the 100g of ice do not have enough energy
and therefore we have to first set equation to see whether the ice can cool the water to 0°C
and see if it still has enough energy to freeze it?

Answer 25

Im not sure about that just suggesting

Answer 26

@Vincent-Lyon.Fr t'es parti :/
@aidanwong he used deduction:
it can't be all solid
it can't be all liquid
so it must be solid+liquid (ice water is always 0C)

Answer 27

@Vincent-Lyon.Fr Au revoir :)
@aidanwong bye :)

Answer 28

hello kc_kennylau
here's whai i tried to do
first of all i brought all the ice at 0degC and calculated the heat required to do this and it came out to be 3075J by the formyla oh heat required in a single phase Q=ms(change in temp.)
next i converted the ice at 0degC to water and found the heat required at that time
by the heat required on state change Q=mL(L=latent hetat of fusion) and it came out to be 33400
next, i brought the temp. of water at 25degC to 0degC and calculated the heaat released
by the formula Q=ms(change in temp.) and now we have 0.3 kg of water at 0degC
so it came out to be 20100 J
now this is less than the heat required so the heat that is required in total = 33400+3075-20100=16375J
the system cannot get energy from anywhere so some of the water from the resultant water at 0degC will get converted to ice
so we'll need the formula Q=mL
now here , Q=16375J and L=3.34x 10^5
it means that 16375 J of heat is needed for m mass of ice to get converted to water
so our final system is now at 0degC and m comes out to be 0.05kg
so we have 0.05kg of ice and 0.25kg of water @ 0degC
if there would enough heat to convert all the water (0.3 kg )@0degC to ice and some ice energy would be needed more, then you would use the formula for heat n the same phase i.e. Q=ms(change in temp)
and remember that this change in tep. is the magnitude so it is always positive so keep it in your mind
and hope this helps you

Answer 29

@aidanwong does this help you? :)

Answer 30

@rajat97 Thanks a million :)

Answer 31

you're welcome @kc_kennylau