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The graph shows the maximum absolute humidity—the maximum amount of water vapor that atmospheric air at sea level can hold—in grams of water vapor per cubic meter (\(\mathrm{g/m^3}\)), for integer-valued temperatures on the Celsius scale from \(1°\mathrm{C}\) through \(41°\mathrm{C}\). When the air contains this maximum amount of water vapor, the air is said to be at its saturation point. In addition, at sea level and at a temperature of \(T°\mathrm{C}\), the density of air containing no water vapor is \(\frac{10^5}{287(T + 273)}\) \(\mathrm{kg/m^3}\) where \(1\) kg \(= 1\) kilogram \(= 1,000\) g.
From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
| Text Component | Literal Content | Simple Interpretation |
|---|---|---|
| Graph subject matter | "The graph shows the maximum absolute humidity" | The chart displays how much water vapor air can hold at different temperatures |
| Definition of maximum absolute humidity | "the maximum amount of water vapor that atmospheric air at sea level can hold—in grams of water vapor per cubic meter (g/m^3)" | Maximum water vapor is measured in grams per cubic meter of air |
| Temperature range | "for integer-valued temperatures on the Celsius scale from \(1°\text{C}\) through \(41°\text{C}\)" | Data covers every whole number temperature from 1 to 41 degrees Celsius |
| Saturation point definition | "When the air contains this maximum amount of water vapor, the air is said to be at its saturation point." | Saturation point means air holds all the water vapor it possibly can |
| Dry air density formula | "at sea level and at a temperature of T °C, the density of air containing no water vapor is \(\frac{10^5}{287(T + 273)} \text{ kg/m}^3\)" | There's a formula to calculate how much dry air weighs at any temperature |
| Unit conversion | "1 kg = 1 kilogram = 1,000 g" | 1 kilogram equals 1,000 grams |
| Chart Component | What's Shown | What This Tells Us |
|---|---|---|
| Chart type | Line graph with circular markers (continuous curve) | The data varies smoothly and continuously across the temperature range |
| X-axis | Temperature in °C from 1 to 41, odd numbers labeled | Covers all integer degrees within the stated range |
| Y-axis | Maximum absolute humidity in g/m^3 from 0 to 55 | Shows water vapor amounts up to 55 grams per cubic meter |
| Curve shape | Steep upward curve, especially rapid above \(30°\text{C}\) | Air's water vapor capacity increases more rapidly at higher temperatures |
| Sample data points | At \(1°\text{C}\): ~4 g/m^3, \(21°\text{C}\): ~16 g/m^3, \(31°\text{C}\): ~30 g/m^3, \(41°\text{C}\): ~51 g/m^3 | Shows more than 12-fold increase in maximum humidity from \(1°\text{C}\) to \(41°\text{C}\) |
At \(37°\text{C}\), and at sea level, the weight of water vapor in \(1 \text{ m}^3\) of air at its saturation point is [BLANK] % of the weight of \(1 \text{ m}^3\) of air containing no water vapor.
What is needed: The percentage ratio (by mass) of saturated water vapor to dry air in \(1 \text{ m}^3\) at \(37°\text{C}\).
The average rate of change of maximum absolute humidity from \(31°\text{C}\) to \(41°\text{C}\) is [BLANK] the average rate of change of maximum absolute humidity from \(11°\text{C}\) to \(21°\text{C}\).
What is needed: Whether the first rate of change (\(31°\text{C}\)–\(41°\text{C}\)) is greater than, less than, or about the same as the second rate (\(11°\text{C}\)–\(21°\text{C}\)).
Blank 1 required a direct calculation of percentage using the graph value and air density formula, resulting in 3.6%. Blank 2 involved comparing the steepness (rate of increase) of the humidity curve at high and low temperature intervals, with the increase being much greater at higher temperatures; thus, the answer is 'greater than'.
Blank 1 and blank 2 are independent: blank 1 asks for a calculation at a single temperature, while blank 2 asks for a comparison of rates over two different temperature intervals. The answer to one does not depend on the answer to the other.