How to determine original temp of water by adding ice using chem moles? or ANY means straightforward!?

Question

Ok, need to design a chemical experiment. I'm given certain amount of water at an unknown temperature and a thermometer that only goes to 40 degrees C. I have a chem lab at my disposal (grad cylinders, 0.001g wieghts, ect) I must find the tempurature of the water. I can use additional water, ice, ect. I need a straighforward way to do this, and record my data. Can I do it using Moles? what equations would I need? is there a way to do it otherwise? Thanks!

Answer 1

You should consider the Heat of Fusion of water (79.7 cal/g) and the Heat Capacity of water 1 cal / gram deg C

I assume the water is above 40 deg C and your thermometer doesn't register above 40. If you add 1 gram of ice to 100 g of water at temp T, the ice will require 80 calories of heat (from the water) to melt. 80 calories would reduce the temperature of the water from T to Tf and would require still more calories to raise the temperature of the melted ice from 0 deg C to Tf

Let w = weight of water and i = weight of ice
Let T = water temperature and Tf = final temperature
Heat Loss = Heat Gain
Heat Gain of Ice = i x 80 + i x Tf
Heat Loss of Water = w x (T - Tf)
i x 80 + i x Tf = w x (T - Tf)

Carry out the experiment in an insulated container. Stir until all of the added ice has melted and record the values of w, i, and Tf. Use the correct amount of water and ice to obtain a temperature between 0 and 40; then solve for T.

Answer 2

Just an idea, It might be theoretically correct but I can't assure It will work on practice.

1.- Take certain amount of water (Maybe 1 liter) and add enough ice until it reaches a temperature which falls well below the max range of the available thermometer, or even better, add an excess of ice until some solid ice remains in equilibrium, so to reach an equilibrium temperature of 0 C which can be checked with the thermometer.

2.- Mix a carefully weighted mass of water at the known temperature (From step 1) with an (also) weighted mass of water at the unknown temperature, mix well and measure the final temperature. All these steps must be done quickly in order to avoid heat losses. Use a Dewar flask of known heat capacity of even better, use a calorimeter if available. To simlify the experiment, you could also use a polistyrene foam cup and disregard the heat absorbed by the container, but this may introduce an undesired uncertainty.

3.- Make the heat balance:

Hkw + Hc= Huw

where

Hkw = heat gained by the water at the known initial temperature

Huw = heat lost by the water at unknown original temperature

Hc = heat absorbed by the container

Remember that for all cases

H=mCp(Tf - To)

Tf = final temperature
To = original temperature

Apply this eq to Hkw and Huw, The final temperature for both cases is known (measured at equilibrium) For Huw the initial temp is what your are trying to find, the rest is pure elemmentary algebra.

Good luck

Answer 3

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