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Nargis786 · Jun 13, 2009, 01:26 PM

The world bank is considering the construction of a vast hydroelectric project to bring fresh water to israel, jordan and palestine. It would involve building a canal from the mediterranean sea to the dead sea, which lies 400m below sea level. The canal would have hydroelectric plsnts to generate electricity for desalination plants at intervals along its length. The desalination plants could produce up to 100 million cubic metres of fresh water per year.
the dead sea is fed by the river jordan, there has been so much extraction of water for drinking and irrigation that in summer the flow of the river has been reduced to little more than a muddy trickle. The dead sea, the salinity of which it makes it the densest body of water on earth, is prone to rapid evaporation and, as more water has been trapped, the level has fallen by 3.0 metres in the last 35 years.

engineers have the following data:

surface area of the dead sea = 880km2
energy required to vaporise 1kg of water = 2.3 x 10^6 J
mean power absorbed by water from sunlight during daylight = 300 W m-2
acceleration of free fall = 9.8 m S-2
Density of sea water in mediterranean sea 1030 kg m-3

using the data supplied answer the following:

a) calculate th power absorbed by the dead sea from the sun during daylight

b) if 60% of the power calculated in a) is used to evaporate water from the dead sea, calculate the mass of water which evaporates in 12 hours of daylight.

c) using the overall fall of the level of the dead sea, estimate the change during te last 35 years in the mass of water in the dead sea.

d) as the water falls from the medterranean sea into the dead sea it loses one form of energy. What frm of energy is this?

e) assume that the propsed project aims to refill the dead sea to its former level in the next 35 years. Estimate the power available from the water falling frm the meditteranean sea into the dead sea.

f) a desalination plant operates on a cylce by evaporating water vapour from sea water and then condensing the waer vapour back into fresh water. Explain why less than 2.3 x 10^6 J are needed for each kg of fresh water produced in the cycle.

g) state and explain 2 physical problems which will make the scheme less efficient

Unknown008 · Jun 14, 2009, 12:09 AM

a) You have the mean power absorbed per metre square, find the power absorbed by the total surface area of the dead sea. (ans: $2.64\times10^{11}W$ )

b) You are given the amount of energy required to evaporate 1 kg of water, find the mass evaporated when 60% of the answer you got in a) is available.(ans: $6.89\times10^4kg$ )

c) Assuming the dead sea to be a prism, (with uniform surface area at all depths), you can find the mass of water decrease during the past 35 years by using the density of water, the surface area and the height given. (ans: I got $2.56\times10^6kg$ )

d) You should know that! The Mediterranean water is above that of the dead sea. This is a change in height, so which energy could that be? Which energy formula includes the height of an object?

e) You now have required mass of water to restore the level of water in the dead sea. So, there's that mass of water which will need to fall from the Mediterranean sea, which is 400 m above the dead sea. Can you now find the energy that the water in the Mediterranean sea contains? It is that energy which will be used in the power plants.

f) You have to realise that the water already contains some energy. Now you have to think where that energy comes from.

g) That, you'll have to think for yourself. How could energy be lost; why will it be lost; the is all the required water available, etc.

Hope it helped! :)

Post back if you have problems still.

Nargis786 · Jun 14, 2009, 05:23 AM

Originally Posted by Unknown008

a) You have the mean power absorbed per metre square, find the power absorbed by the total surface area of the dead sea. (ans: $2.64\times10^{11}W$ )

b) You are given the amount of energy required to evaporate 1 kg of water, find the mass evaporated when 60% of the answer you got in a) is available.(ans: $6.89\times10^4kg$ )

c) Assuming the dead sea to be a prism, (with uniform surface area at all depths), you can find the mass of water decrease during the past 35 years by using the density of water, the surface area and the height given. (ans: I got $2.56\times10^6kg$ )

d) You should know that! The Mediterranean water is above that of the dead sea. This is a change in height, so which energy could that be? Which energy formula includes the height of an object?

e) You now have required mass of water to restore the level of water in the dead sea. So, there's that mass of water which will need to fall from the Mediterranean sea, which is 400 m above the dead sea. Can you now find the energy that the water in the Mediterranean sea contains? It is that energy which will be used in the power plants.

f) You have to realise that the water already contains some energy. Now you have to think where that energy comes from.

g) That, you'll have to think for yourself. How could energy be lost; why will it be lost; the is all the required water available, etc.

Hope it helped! :)

Post back if you have problems still.

thanks a lot for your help i am now able to understand it better but i am still having problems with D, E, F and G. I do not really understand these properly. E is asking for me to estimate the power available from the water falling from the mediterrranean sea into the dead sea.

also with A, B and C could you please show me the working out to how you got the answers so i am able to understand it fully. Thank you for your help.

Unknown008 · Jun 14, 2009, 05:47 AM

Ok, these are simple maths... and test your understanding of the questions...

a)

surface area of the dead sea = $880km^2$
mean power absorbed by water from sunlight during daylight = $300 W m^{-2}$

The mean power absorbed is 300Wm^-2, so for each metre square, the water gains 300 watts of power. Since the lake is 880 km^2, the power you get is:

$Power=300 \times 880 \times 1000000= 2.64\times10^{11}$

Since 880 is equivalent to 880*1000000 m^2.

b) Energy used for evaporation = 60% of (2.64 x 10^11) W = 1.584 x 10^11 W

Since 2.3 x 10^6 J are required to evaporate 1 kg of water and you have $1.584\times10^{11} \times 12\times3600 = 6.84\times10^{18}J$ available, you can evaporate $\frac{6.84\times10^{18}}{2.3\times10^6 } = 2.98\times10^{12}kg$ of water.

::::::(just found a mistake I made :o, forgot to convert power to energy:::::

c) Since there is a decrease in height of 3 m, and the surface area of the lake is 880, 000, 000 m^2, the volume is $880000000\times 3=2.64\times10^9 m^3$ .

Using the density, you have 1030 kg/m^3, you have $1030 \times 2.64\times10^9=2.7192\times10^{12} kg$

Nargis786 · Jun 14, 2009, 05:50 AM

Originally Posted by Unknown008

Ok, these are simple maths... and test your understanding of the questions...

a)

The mean power absorbed is 300Wm^-2, so for each metre square, the water gains 300 watts of power. Since the lake is 880 km^2, the power you get is:

$Power=300 \times 880 \times 1000000= 2.64\times10^{11}$

Since 880 is equivalent to 880*1000000 m^2.

b) Energy used for evaporation = 60% of (2.64 x 10^11) W = 1.584 x 10^11 W

Since 2.3 x 10^6 J are required to evaporate 1 kg of water and you have $1.584\times10^{11} \times 12\times3600 = 6.84\times10^{18}J$ available, you can evaporate $\frac{6.84\times10^{18}}{2.3\times10^6 } = 2.98\times10^{12}kg$ of water.

::::::(just found a mistake I made :o, forgot to convert power to energy:::::

c) Since there is a decrease in height of 3 m, and the surface area of the lake is 880, 000, 000 m^2, the volume is $880000000\times 3=2.64\times10^9 m^3$ .

Using the density, you have 1030 kg/m^3, you have $1030 \times 2.64\times10^9=2.7192\times10^{12} kg$

thank you i understand now but can you please help me on the other questions i posted which are D, E, F, G

Unknown008 · Jun 14, 2009, 05:59 AM

d) This refers to the POTENTIAL ENERGY of the water. The Mediterranean sea being above the dead sea, it loses gravitational potential energy and gains kinetic energy, which will be used in power plants.

e) The mass (of water) you need is the mass that was lost, therefore 2.7192 x 10^12 kg.

You know the formula for gravitational potential energy, E=mgh?

Here, you use that;

$E_p=2.7192\times10^{12} \times 9.8 \times 400 = 1.07\times10^{16} J$

f) remember the water absorbs 60% of the energy from the sun? Well, the remaining 40% stays in the water, making it warmer. Since the water is warmer, you need less energy to heat it for evaporation, right?

g) If you want to produce water, the system will never be 100% efficient (anyway, that applies to everything that include efficiency) This is because some of the kinetic energy is converted to sound. Then, what if there is a period when the Mediterranean's sea water level is lower than usual, the rate of flow of water will decrease, or even stop. Then, you also have the fact that people may be using water from the dead sea, meaning that you'll need more water so that is restores the previous lost water. You can try to think about others.

Hope it helped!

(btw, you can rate my answer, and say you agree or disagree, depending if my answer helped or not)

Unknown008 · Jun 14, 2009, 06:00 AM

Phew! :p, got them done. These take quite some time to type...