The graph shows the maximum absolute humidity—the maximum amount of water vapor that atmospheric air at sea level can hold—in...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

The maximum absolute humidity of air increases exponentially with temperature at sea level. Between \(1°\mathrm{C}\) and \(21°\mathrm{C}\), water vapor capacity rises modestly, but above \(30°\mathrm{C}\), the air's capacity for water vapor increases dramatically. From \(31°\mathrm{C}\) to \(41°\mathrm{C}\), the additional water vapor air can hold grows three times faster than from \(11°\mathrm{C}\) to \(21°\mathrm{C}\) (\(21\text{g/m}³\) vs \(7\text{g/m}³\) increase). At \(37°\mathrm{C}\)—the body's typical temperature—water vapor at saturation is about \(3.6\%\) of the weight of \(1 \text{ m}^3\) of dry air. The chart highlights that hot air can carry much more moisture than cold air, and the underlying dataset provides values at each integer temperature from \(1°\mathrm{C}\) to \(41°\mathrm{C}\) for full quantitative analysis.

Step-by-Step Solution

Question 1: Water Vapor Percentage by Weight at 37°C

Complete Statement:

At \(37°\mathrm{C}\), and at sea level, the weight of water vapor in \(1 \text{ m}^3\) of air at its saturation point is ___%of the weight of \(1 \text{ m}^3\) of air containing no water vapor.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: At \(37°\mathrm{C}\), and at sea level
  • Meaning: This sets the specific temperature and conditions for the calculation.
  • Relation to Chart: We need to find the value at \(37°\mathrm{C}\) from the chart (maximum absolute humidity).
  • Important Implications: All calculations will use values at \(37°\mathrm{C}\) from the provided data/chart.
• Statement Breakdown 2:
  • Key Phrase: weight of water vapor in \(1 \text{ m}^3\) of air at its saturation point
  • Meaning: The amount (in grams) of water vapor at maximum (saturated) humidity at this temperature in one cubic meter of air.
  • Relation to Chart: Read the maximum absolute humidity at \(37°\mathrm{C}\) from the chart/table.
  • Important Implications: This gives us the numerator in the percentage calculation.
• What is needed: At \(37°\mathrm{C}\), the percentage of the mass of saturated water vapor per m³ compared to the mass of dry air per m³.

Solution:

• Condensed Solution Implementation:
  Use the given dry air density equation and saturated vapor data from the chart to compute the percentage.
• Necessary Data points:
  Max absolute humidity at \(37°\mathrm{C}\): \(40 \text{ g/m}^3\). Dry air density at \(37°\mathrm{C}\) from formula: \(\frac{10^5}{287 × (37 + 273)}\).
  • Calculations Estimations:
    Calculate dry air density: \(\frac{10^5}{287 × 310} = \frac{100000}{88970} ≈ 1.12 \text{ kg/m}^3 = 1120 \text{ g/m}^3\). Calculate percentage: \(\frac{40}{1120} × 100\% ≈ 3.57\%\).
  • Comparison to Answer Choices:
    Choices are typically to one decimal. \(3.57\%\) rounds to \(3.6\%\), so the answer is 3.6.

FINAL ANSWER Blank 1: 3.6

Question 2: Comparing Rates of Change of Maximum Absolute Humidity

Complete Statement:

The average rate of change of maximum absolute humidity from \(31°\mathrm{C}\) to \(41°\mathrm{C}\) is ___ the average rate of change of maximum absolute humidity from \(11°\mathrm{C}\) to \(21°\mathrm{C}\).

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: average rate of change of maximum absolute humidity from \(31°\mathrm{C}\) to \(41°\mathrm{C}\)
  • Meaning: How much, on average, the humidity increases for each \(1°\mathrm{C}\) in this temperature range.
  • Relation to Chart: Find the values at \(31°\mathrm{C}\) and \(41°\mathrm{C}\) in the chart, subtract, and divide by the temperature difference.
• Statement Breakdown 2:
  • Key Phrase: average rate of change of maximum absolute humidity from \(11°\mathrm{C}\) to \(21°\mathrm{C}\)
  • Meaning: How much, on average, the humidity increases for each \(1°\mathrm{C}\) in the lower temperature range.
  • Relation to Chart: Find the values at \(11°\mathrm{C}\) and \(21°\mathrm{C}\) in the chart, subtract, and divide by the temperature difference.
• What is needed: Whether the average rate of increase in humidity per degree is greater at higher or lower temperatures.

Solution:

• Condensed Solution Implementation:
  Calculate the difference in humidity over each interval and divide by the number of degrees (10), then compare the two results.
• Necessary Data points:
  From the chart: \(11°\mathrm{C} = 9 \text{ g/m}^3\), \(21°\mathrm{C} = 16 \text{ g/m}^3\), \(31°\mathrm{C} = 30 \text{ g/m}^3\), \(41°\mathrm{C} = 51 \text{ g/m}^3\).
  • Calculations Estimations:
    From \(11°\mathrm{C}\) to \(21°\mathrm{C}\): \(\frac{16 - 9}{10} = 0.7 \text{ g/m}^3\) per \(°\mathrm{C}\). From \(31°\mathrm{C}\) to \(41°\mathrm{C}\): \(\frac{51 - 30}{10} = 2.1 \text{ g/m}^3\) per \(°\mathrm{C}\).
  • Comparison to Answer Choices:
    2.1 is much greater than 0.7, so the correct comparison is 'greater than.'

FINAL ANSWER Blank 2: greater than

Summary

Blank 1 is solved by comparing the mass of saturated water vapor at \(37°\mathrm{C}\) to the mass of dry air at the same temperature, giving \(3.6\%\). Blank 2 is solved by comparing the average rate of change of maximum absolute humidity in different temperature ranges; the rate between \(31°\mathrm{C}\) and \(41°\mathrm{C}\) is much greater than that between \(11°\mathrm{C}\) and \(21°\mathrm{C}\).

Question Independence Analysis

The two blanks are independent: Blank 1 asks for a ratio at a single temperature (\(37°\mathrm{C}\)), while Blank 2 compares average rates of humidity change in two separate temperature intervals. Solving one does not require information from the other.