[fruitbasket]

can someone help me solve this problem:

water expands when it freezes.  How much work does 100.g of water do when it freezes at 0 degree C and bursts a water pipe that exerts an opposing pressure of 1070 atm?  The densities of water and ice at 0 degree C are 1.00 g per cubic cm and 0.92 per cubic cm, respectively.

the answer in the book is -0.9 kJ

[Yggdrasil]

What formulas do you know for how to calculate work?  Can you calculate by how much volume the water expands when it freezes?

[fruitbasket]

work = - (external pressure) (changes in Volume)

+ i figured that the volume of ice is 9% larger than the volume of water:

density = mass/volume

Volume of water: 1.00 g/cm^3  = 100.g / V
                                         V  =  100. cm^3
Volume of ice: .92 g/cm^3 = 100. g/ V
                                  V  =  109 cm^3
Therefore, ice is 9% or 9 cm^3  larger than water

+ i tried to find the answer using the work formula...for some reason i couldnt get -0.9 kJ!!!

[english]

work = - (external pressure) (changes in Volume)

+ i figured that the volume of ice is 9% larger than the volume of water:

density = mass/volume

Volume of water: 1.00 g/cm^3  = 100.g / V
                                         V  =  100. cm^3
Volume of ice: .92 g/cm^3 = 100. g/ V
                                  V  =  109 cm^3
Therefore, ice is 9% or 9 cm^3  larger than water

+ i tried to find the answer using the work formula...for some reason i couldnt get -0.9 kJ!!!

100.g of water in liquid form is around .01 cm³, in solid form around .0092 cm³.

You got your volumes wrong.
 

[fruitbasket]

oh...maybe that's why i couldnt get the freakin answer...thank you..but how did u calculate the volumes of water and ice?

[Borek]

100.g of water in liquid form is around .01 cm³, in solid form around .0092 cm³.

Huh?

[Yggdrasil]

Fruitbasket got the change in volume right.  So, to get the work, you need to use the formula:

work = - (external pressure)*(change in volume)

To get 9630 atm*cm³.  Note that the units of the answer are not in kJ.  If you convert atm*cm³ to kJ you should get the right answer (hint: 1 atm = 101.3 kPa, 1Pa = 1N/m², 1J = 1N*m)

[english]

Well now I am confused because you are saying that water and ice at 0°C have two different densities.  At 0°C, water is ice.

 

[Yggdrasil]

At 0^oC, liquid water and ice are at equilibrium.  Hence, you can have water and ice.

[english]

At 0^oC, liquid water and ice are at equilibrium.  Hence, you can have water and ice.

Then ice is in greater concentration at equilibrium right?  I never learned this before.   

[Yggdrasil]

Ice is a solid so its activity is constant and pure water will also have a constant activity (activity is the equivalent of concentration in thermodynamics).  So if you put x g of pure ice and y g of pure water in a container and keep the temperature of the container at a constant 0^oC, you will have x g of ice and y g of water after an arbitrary amount of time.

[english]

Right I remember about pure solids and pure liquids at equilibirum.  Thanks for the refresher.