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A sauna has 7.0 m3 of air volume, and the temperature is 90°C. The air is perfectly dry
Chapter 13, Problem 96GP(choose chapter or problem)
Problem 96GP
A sauna has 7.0 m3 of air volume, and the temperature is 90°C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3)
Table 13–3
Saturated Vapor Pressure of Water
Temperature (ºC) |
Saturated Vapor Pressure |
|
torr (= mm-Hg) |
Pa (= N/m2) |
|
–50 |
0.030 |
4.0 |
–10 |
1.95 |
2.60 × 102 |
0 |
4.58 |
6.11 × 102 |
5 |
6.54 |
8.72 × 102 |
10 |
9.21 |
1.23 × 103 |
15 |
12.8 |
1.71 × 103 |
20 |
17.5 |
2.33 × 103 |
25 |
23.8 |
3.17 × 103 |
30 |
31.8 |
4.24 × 103 |
40 |
55.3 |
7.37 × 103 |
50 |
92.5 |
1.23 × 104 |
60 |
149 |
1.99 × 104 |
70† |
234 |
3.12 × 104 |
80 |
355 |
4.73 × 104 |
90 |
526 |
7.01 × 104 |
100‡ |
760 |
1.01 × 104 |
120 |
1489 |
1.99 × 104 |
150 |
3570 |
4.76 × 104 |
†Boiling point on summit of Mt. Everest.
‡Boiling point at sea level.
Questions & Answers
QUESTION:
Problem 96GP
A sauna has 7.0 m3 of air volume, and the temperature is 90°C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3)
Table 13–3
Saturated Vapor Pressure of Water
Temperature (ºC) |
Saturated Vapor Pressure |
|
torr (= mm-Hg) |
Pa (= N/m2) |
|
–50 |
0.030 |
4.0 |
–10 |
1.95 |
2.60 × 102 |
0 |
4.58 |
6.11 × 102 |
5 |
6.54 |
8.72 × 102 |
10 |
9.21 |
1.23 × 103 |
15 |
12.8 |
1.71 × 103 |
20 |
17.5 |
2.33 × 103 |
25 |
23.8 |
3.17 × 103 |
30 |
31.8 |
4.24 × 103 |
40 |
55.3 |
7.37 × 103 |
50 |
92.5 |
1.23 × 104 |
60 |
149 |
1.99 × 104 |
70† |
234 |
3.12 × 104 |
80 |
355 |
4.73 × 104 |
90 |
526 |
7.01 × 104 |
100‡ |
760 |
1.01 × 104 |
120 |
1489 |
1.99 × 104 |
150 |
3570 |
4.76 × 104 |
†Boiling point on summit of Mt. Everest.
‡Boiling point at sea level.
ANSWER:Solution 96GP
Step 1 of 3:
Consider a sauna of volume V is at temperature T and the relative humidity is increased to 10%. We are going to find the amount of water (m) to be evaporated to achieve the humidity.
The volume of the sauna V = 7 m3
The temperature 90°C = 363 K
The saturated pressure corresponding to T (Psat)= 7.01 x 104 Pa
The relative humidity RH =10% = 0.1
The molar mass of water molecule M = 18 x 10-3 kg/mol
The gas constant R = 8.3145 m3.Pa.K-1.mol-1