Homework #2         Glaciology and the Cryosphere, GEOL 4888, 

Spring 2022         Humphrey

1.    Table showing the typical pressure, volume distribution in the earth’s atmosphere.

Height (meters)

Pressure (105 Pa)

Cubic m of air per kg of air

0

1.01

.82

2000

.795

.99

4000

.617

1.22

6000

.472

1.51

8000

.356

1.90

10000

.265

2.42

 

 

 

 

An important aspect of the cryosphere is the temperature LAPSE RATE that creates colder temperatures at altitude. With this table we can get a sense of the temperature structure in the air above us if we assume the air is dry, well mixed and the air is a perfect gas.  These assumptions are only approximately true.  The moisture in the air tends to make the air a little warmer, while poor mixing tends to make entire parcels of air either warmer or cooler.  However, these assumptions will give us a reasonable estimate of temperature.  We will use the relationship for an ideal gas between pressure (P), volume (V) and temperature (T): PV = nRT.  If we assume the temperature at sea level is 15C (288K, note the equation requires Kelvin degrees), you can calculate a value for the constant ‘nR’, and use the equation to calculate the temperature at various elevations.

Your job: Plot the temperature structure of our atmosphere.  Predict the temperature outside most airlines? (they typically fly around 11,000m).  Check on the web for the outside temperature at 35,000ft.

 

2.    Questions on the Clausius-Clapeyron slope of the ice phase diagram.  Now you know how to calculate the pressure inside a glacier:

A Calculate the pressure melting point (the temperature at which the ice would melt) under the ice in central Greenland, assume the ice is 3000m thick?

B Assume the ice is at this calculated temperature, and that it has been for 1000s of years; is it melting due to the pressure?

 

3.    When snow is compressed to firn and then to ice, pore close off occurs at about 830kg/m3, while glacier ice is about 920kg/m3.  Pore close-off means that air can no longer move from pore to pore and is trapped.  So how many kilograms of air are there in a m3 cube of glacier ice?  (This is the air that bubbles out of glacier ice when it is melted in drinks!)