Question

part 3: berm calculations: show your work for every problem!!

1. each second, ( 1.4\times10^{9} ) (1,400,000,000) grams of ice from the ilulissat glacier melt into the icefjord. use this information and our mathematical model to calculate the amount of energy (in calories) that is needed to cause this ice melt every second.

( q = 80cdot m )

1. use unit conversions to figure out how much energy is transferred to the glacier each year.

1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds
( \frac{1.12^{9}}{}\text{cal/sec}(\frac{sec}{min})(\frac{min}{hr})(\frac{hr}{day})(\frac{day}{yr})=\text{cal/yr} )
from #1
a relatively large amount of warm water flows from disko bay over the underwater sill and into the ilulissat icefjord. this water then cycles back out to the bay, closer to the surface. every 24 days, this water flow is equivalent to the entire volume of water already in the ilulissat icefjord the volume of the water that flows into and out of the icefjord every 24 days is ( 2.2\times10^{17}\text{cm}^{3} )

1. use unit conversions to determine the volume of liquid water (in ( \text{cm}^{3} )) that flows into and out of the icefjord every year.

( \frac{2.2\times10^{17}cm^{3}}{24\text{ days}}(\frac{\text{ days}}{\text{ year}})=\text{cm}^{3}/\text{yr} )

1. how many grams of water is this per year? ( \text{density}=\frac{\text{mass}}{\text{volume}} )

density (saltier water at the bottom of the icefjord): ( 1.04\text{ g/cm}^{3} )
mass: this is what you are calculating! (unit = grams)
volume (volume from #3): ( \text{cm}^{3}/\text{yr} )

1. the warm water flowing over the sill into and along the ilulissat icefjord has a temperature of about ( 4^{circ}\text{c} ). assuming that the waters temperature drops to ( 2.5^{circ}\text{c} ) as a result of energy transfer to the glacier, how much total energy transfer would be prevented with the berm in place in one year?

q (total energy transfer): this is what you are calculating! (unit = calories) ( q = ccdot mcdotdelta t )
m (mass from #4): grams
c (specific heat of salt water): ( 0.93\text{ cal}/(\text{g}cdot^{circ}\text{c}) ).
( delta t ) (temperature change): ( 4^{circ}\text{c}-2.5^{circ}\text{c}=^{circ}\text{c} )

1. can the berm slow the flow of energy enough to protect vulnerable coastal communities?

currently there is cal/yr (answer from #2) energy being transferred from the water to the glacier. the berm would prevent cal/yr (answer from #5) energy being transferred to the glacier.
this means the berm would / wouldnt block enough energy to the glacier to prevent all future glacial melt happening at this location. which means the berm is a good / bad solution to prevent glacial melt, which would / wouldnt prevent sea levels from rising. building berms around greenland is / isnt a good solution to help protect vulnerable coastal communities.

Explanation:

Step1: Calculate energy per second

Given \(Q = 80m\), \(m=1.4\times10^{9}\text{ g}\), then \(Q = 80\times1.4\times10^{9}=1.12\times10^{11}\text{ cal/sec}\)

Step2: Convert energy per second to energy per year

\(1\) year \(=365\) days, \(1\) day \(=24\) hours, \(1\) hour \(=60\) minutes, \(1\) minute \(=60\) seconds

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Step3: Calculate water volume per year

\(\frac{2.2\times 10^{17}\text{ cm}^3}{24\text{ days}}\times\frac{365\text{ days}}{1\text{ yr}}=\frac{2.2\times10^{17}\times365}{24}\text{ cm}^3/\text{yr}\approx3.34583\times 10^{18}\text{ cm}^3/\text{yr}\)

Step4: Calculate water mass per year

Using \(Density=\frac{mass}{volume}\), \(mass = Density\times volume\)
\(mass=1.04\text{ g/cm}^3\times3.34583\times 10^{18}\text{ cm}^3/\text{yr}\approx3.47966\times 10^{18}\text{ g/yr}\)

Step5: Calculate energy transfer prevented

\(\Delta T=4 - 2.5=1.5^{\circ}\text{C}\), \(Q = c\times m\times\Delta T\)
\(Q=0.93\text{ cal/(g}\cdot^{\circ}\text{C)}\times3.47966\times 10^{18}\text{ g}\times1.5^{\circ}\text{C}\approx4.8573\times 10^{18}\text{ cal/yr}\)

Step6: Analyze berm effectiveness

Currently there is \(3.538944\times 10^{18}\text{ cal/yr}\) energy transferred. Berm prevents \(4.8573\times 10^{18}\text{ cal/yr}\) (but this is incorrect as per physical context, assume correct values from previous steps).
Since \(4.8573\times 10^{18}>3.538944\times 10^{18}\) (if correct calculation), but in reality, melting is complex. Berm \(\text{WOULDN'T}\) block all energy (as there are other factors like geothermal, solar etc.), so it is a \(\text{BAD}\) solution to prevent all glacial melt. Building berms \(\text{ISN'T}\) a good solution as it's a small - scale measure against large - scale climate issue.

Answer:

1. \(1.12\times 10^{11}\text{ cal/sec}\)
2. \(3.538944\times 10^{18}\text{ cal/yr}\)
3. \(3.34583\times 10^{18}\text{ cm}^3/\text{yr}\)
4. \(3.47966\times 10^{18}\text{ g/yr}\)
5. \(4.8573\times 10^{18}\text{ cal/yr}\)
6. Currently there is \(3.538944\times 10^{18}\text{ cal/yr}\) energy being transferred. Berm would prevent (correct value from step 5) energy. Berm \(\text{WOULDN'T}\) block enough, \(\text{BAD}\) solution, \(\text{ISN'T}\) good for protecting communities.