(adsbygoogle = window.adsbygoogle || []).push({}); Intro Thermodynamics--put ice in water

1. The problem statement, all variables and given/known data

(a) Two 45 g ice cubes are dropped into 290 g of water in a thermally insulated container. If the water is initially at 25°C, and the ice comes directly from a freezer at -15°C, what is the final temperature at thermal equilibtrium? (Neglect the heat capacity of the glass.)

(b) What is the final temperature if only one ice cube is used?

2. Relevant equations

Q_out=Q_in

For temperature change without phase change:

[tex]Q=cm\Delta T[/tex]

For phase change:

[tex]Q=Lm[/tex]

^{o}C + 273.15 = K

3. The attempt at a solution

I solved part a; as the energy needed to melt the ice is greater than the heat available from the water the system stabilizes at the melting/freezing point of water.

For part b, to check if the water has enough energy to melt the ice, I computed (where the supscript i stands for ice) [tex]c_im_i\Delta T + L_im_i = (2220 \frac{J}{kg K})(0.045 kg)(288.15 K - 273.15 K) + (333000 \frac{J}{kg})(0.045 kg) = 16483.5 J [/tex]

I had found in part a that the energy that the water can give off before freezing is [tex]c_wm_w \Delta T = (4190 \frac{J}{kg K})(0.290 kg)(298.15) = 30377.5 J[/tex].

Since Q_i < Q_w, the ice will melt completely and the water temperature will rise. Thus, my equation for part b ought to read as follows:

[tex]c_im_i(T_f-T_{ice initial}) + L_im_i = -c_wm_w(T_f-T_{water initial})[/tex]

Yes, I should have done algebra here, but I lazily chose (and continue to choose) not to; I just plug and play as long as I can. Also, since we're always dealing with Delta T rather than T proper, converting to Kelvins will end up cancelling, so I left everything in Celcius (which is what the problem asks for, anyways). So:

[tex](2220)(0.045)(T_f - (-15)) + (333000)(0.045) = -(4190)(0.290)(T_f - 25)[/tex]

This arithmetics out to [tex]99.9T_f + 1498.5 = -1215.5T_f + 30377.5[/tex]

Get all the T_f's onto one side, divide by their coefficient, and get T_f = 21.96 degrees Celcius.

Then WebAssign says that that is the incorrect answer. And (as you may have concluded from the fact that I'm posting this at all) I CAN'T FIND MY ERROR!

P.S. This belongs in the suggestion forum, but can a great and holy administrator maybe add an icon? The :banging head against brick wall: icon?

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# Homework Help: Intro Thermodynamics-put ice in water

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