Water Vapor and Phase State Changes
Water Vapor and Phase State Changes
Part I. Specific Heat
Specific heat is the amount of energy required to raise 1 gram of a substance 1 degree Celsius. Different substances have different specific heat values.
Table 1. Specific Heat
Substance
Specific Heat (in calories)
Water
1
Wet mud
.6
Water vapor
.5
Ice
.5
Dry sandy clay
.33
Dry air
.24
Granite
.19
The relationship between calories and temperature can be expressed mathematically:
Q = cmDT
Q= calories added
c = specific heat of substance
m = mass of substance (grams)
DT = temperature change
In words, calories added = specific heat of the substance times the mass of the substance (in grams) times the temperature change.
1. How many calories must be added to 1 gram of granite to increase its temperature 5 degrees Celsius?
2. How many calories must be added to 1 gram of wet mud to increase its temperature 5 degrees Celsius?
We can rearrange the formula to solve for temperature change given an increase/decrease in calories.
3. What is the temperature change of 1 gram of granite if we add .95 calories to it?
4. What is the temperature change of 1 gram of wet mud if we add 3 calories to it?
Part II. Latent Heat
Remember, when calories are added to water, each calorie increases the temperature of 1 gram of water 1 degree Celsius. Eventually the water’s temperature will reach 100 degrees Celsius. At this point, however, the next calorie does not increase the temperature of the water. Instead, this calorie and an additional 539 more calories contribute to the phase state change of water from liquid to gas. These 540 calories (for 1 g of water) are called the latent heat of vaporation/condensation (Hv).
Q = mHv
required
m = mass (grams)
Hv= latent heat of vaporization / condensation
5. You have 14 grams of water at 100 degrees Celsius. How many calories are required to vaporize this water?
Notice from Table 1. that it takes .5 calories to heat 1 gram of ice 1 degree Celsius. When successive calories are added to 1 gram of ice, each calorie increases the temperature of the ice 2 degrees Celsius. Eventually the ice reaches 0 degrees Celsius. The next calorie, though, does not increase the temperature of the ice; rather it helps to induce a phase state change. This calorie, and 79 more calories, causes the ice to change to a liquid (melt). These 80 calories are called the latent heat of melting Hm.
Q = mHm
required
m = mass (grams)
Hm= latent heat of melting
6. You have 50 grams of water at 100 degrees Celsius. How many calories are required to vaporize this water?
7. You have 50 grams of ice at 0 degrees Celsius. How many calories are required to melt this ice?
Part III. Relative Humidity
Relative humidity is the amount of water vapor present in the air relative to the amount of that would be present if the air were saturated. It is expressed as a percentage. Relative Humidity = (Water vapor content/Water vapor capacity) X 100. Recall that air’s water vapor capacity is dependent on its temperature.
Table 2. Water Vapor Capacity of Air
Temperature (deg Celsius)
Capacity (g/kg) [How many grams of water it takes to saturate a parcel – 1 kg – of air]
-40
.1
-30
.3
-20
.75
-10
2
0
3.5
5
5
10
7
15
10
20
14
25
20
30
26.5
35
35
40
47
8. Plot the information above in a line graph, with temperature on your X-axis and capacity on your y-axis.
9. How does warm air’s capacity to hold water vapor compare to cold air’s capacity to hold water vapor?
10. One kilogram of air contains 5 grams of water vapor. Assume that it can contain 10 grams of water vapor. What is the relative humidity (RH) of the air? Show the formula you use to calculate its RH.
11. Does relative humidity increase or decrease as temperature rises?
