Lava problem As a geologist with knowledge of lava, you are asked to assess the

Question

Lava problem

As a geologist with knowledge of lava, you are asked to assess the probability of success of a defense against lava of this kind.

A) THe LaVa flow is confined between buildings 30m apart so thay you must cool an area 30 m x 150m. The lava flow needs to solidify to a depth of 1 meter in order to create a crust sufficiently strong and extensive to resist the pressure from upstream of the still molten and flowing lava. Estimate the Volume of the lava (in m^3).

B) The Density of Lava is 3,000 kg/m^3. Calculate the total mass in (kg) of lava that must be chilled.

C) the temperature of the lava flow is 1050 degrees celsius. For the lava to solidify, it must be cooled to 250 degrees celsius. It requires 840 J of energy be removed from 1 kg of lava to cool it by 1 degree celsius (specific heat of 840 J/kg/degree celsius). How much energy needs to be removed from the lava to stop the flow?

d) One Kilogram of water can absorb 2.64 x 10^6 J before it turns into steam. Assume that once the water turns to steam, it escapes into the atmosphere and cannot further absorb heat from the lava. 1 Gallon of water weighs 3.8 kg. Calculate the amount of water needed to stop the lava flow both in kg and in gallons.

e) Assume that you have 10 fire trucks and that each truck can pump 1500 gallons per minute onto the lava. Calculate how long would take foe the fire fighters to pump water to stop the lava flow.

f) Assume that each helicopter can dropp 500 gallons of water at a time. Calculate how many helicopter drops it would take to stop the lava flow.

g) Based on the results from e and f, how would yo assess the probability of success of a defense against lava flow using fire tracks and helicopters? Remember in the movie this happens within minutes.

Explanation / Answer

A)

Density of Lava = 3,000 kg/m3

Volume of lava= 30mX150mX1m=4500m3

B)

mass=densityxvolume = 3,000*4500=1.35x107kg

C)

The temperature of the lava flow = 1050oC

For lava to solidify, it must be cooled to 250 degrees celsius.

It requires 840 J of energy be removed from 1 kg of lava to cool it by 1 degree celsius (specific heat of 840 J/kg/degree celsius).

So 1.35x107kg lava to cool by 1oC requires = 1.35x107 * 840 =1134x107J/kg/degree celsius

For lava to solidify, it must be cooled to 250 degrees celsius.

1050oC lava when cooled to 250oC , (1050-250) 800oC heat will be removed from it.

It requires 1134x107*800 =90.72x1011J of energy

D)

2.64 x 106J is absorbed by 1kg of water

So 90.72x1011J is absorbed by = 90.72x1011x1kg/2.64 x 106J = 34.36x105kg

3.8kg =1 Gallon

34.36x105kg = 34.36x105/3.8 = 9.042x105 Gallon

To stop the lava flow 34.36x105kg or 9.042x105 Gallon of water is needed.

e)

We have 10 fire trucks. Each truck can pump 1500 gallons per minute.

10 fire trucks can pump 1500*10 gallons/minute= 15000Gallons/minute

To stop the lava flow 9.042x105 Gallon of water is needed.

So 10 fire trucks have to pump (9.042x105 Gallon*1min/15000Gallon) time =60.3minutes=1hour

f)

500gallon - 1 helicopter

To stop the lava flow 9.042x105 Gallon of water is needed.

So 9.042x105 Gallon * 1 helicopter/500 Gallon = 0.01808x105 = 1808 helicopters should drops water to stop the lava flow.

g)

10 fire trucks have to pump water almost 1 hour or around 1808 helicopters should drops water to stop the lava flow. In real the probability of success is very low.

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