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Difficulty:
95%
(hard)
Question Stats:
54%
(03:42)
correct 46%
(03:25)
wrong
based on 577
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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 (g/m^3), for integer-valued temperatures on the Celsius scale from 1°C through 41°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 °C, the density of air containing no water vapor is \(\frac{10^5}{287(T + 273)}\) 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.
At 37°C, and at sea level, the weight of water vapor in 1 m^3 of air at its saturation point is % of the weight of 1 m^3 of air containing no water vapor.
The average rate of change of maximum absolute humidity from 31°C to 41°C is the average rate of change of maximum absolute humidity from 11°C to 21°C.
The units don’t play much of a role in this question. The units are the same and there’s no conversion needed, you only have percentage conversion.
I solved this on the back of the napkin without a calculator or the napkin. Of course I was casually looking on my phone without timing myself for the time pressure of the question but it is possible to solve it without the calculator. You should make a challenge for yourself to figure out how to solve every DI question without a calculator. I don’t mean to force yourself to do calculations in your head but figure out if there is a shortcut that would allow you to solve the question without doing calculations.
1. If you look at this scary equation you will notice that at the top you have 100,000 in the numerator and denominator is basically going to be 300×300. I don’t think you need to have a more precise calculation there.
This means the weight of air going to be 1.1 kg approx. Since it’s over 1 , and water vapor Weighs 40 g, it’s not going to be 4% it’s going to be approx 10% less than 4% but not quite as little as 3.2% which is 20% less.
I hesitated a little because it was slightly over 40 g but 40 to 41 It’s only a 2 1/2% change whereas from one to 1.1 is a 10% change. So the final answer would likely be slightly higher than 3.6. Maybe it’s 3.7 but still less than 4% and closer to 3.6%
The second question is fairly easy because you just look at the chart and you see the rate of change and it’s clearly greater because it’s exponential or at least it looks to me like that and that was the correct answer 😇
The key to this question was a good understanding between the numerator and denominator so you understand what happens when you divide a number by 1.1 or 0.9. Key for mental math.
Interesting question it took 5mins to solve this question, I got it right once I understood the first part. Some calculations using the calculator.....the second part is easy if you take the slope and the compare the angle of the two lines which will indicate that rate of change from 31-41 degrees celsius is greater.
It took me longer than average to solve this problem as I felt a little overwhelmed with the amount of information that was thrown at me.
Interesting question it took 5mins to solve this question, I got it right once I understood the first part. Some calculations using the calculator.....the second part is easy if you take the slope and the compare the angle of the two lines which will indicate that rate of change from 31-41 degrees celsius is greater.
It took me longer than average to solve this problem as I felt a little overwhelmed with the amount of information that was thrown at me.
Hi, Can you elaborate step by step how you went about this question?
Took around 5 min to solve the question. the second part was easier since i just compared the slopes but the first part took some time and i had to use the calculator to solve it. Is there any other way (other than directly calculation the percentage change) to solve it?
hrishi84 - The first part of the question stem is tricky, but if you read it carefully, you can figure it out.
I'll try to break it down: a. At 37C, "the weight of water vapor in 1m^3 of air at its saturation point"- The term "saturation point" can also be interpreted as Maximum Absolute Humidity. Hence, we need to locate the "Absolute Humidity" at 37C on the graph, which equates to 41 g/m^3
b. At 37C, "the weight of 1m^3 of air containing no water vapor"- This is where you need to apply the formula given in the description part of the question stem. Apply the Formula for T=37, you will get 10^5/(287)(37+273)= 10^5/287*310 kg/m^3
To obtain the desired %, convert kg to g or g to kg as the units differ for both values.
At 37°C the weight of water vapor in \(1m^3\) is around \(40\)g of absolute humidity.
At 37°C the weight of air containing no water vapor is \(\frac{10^5}{287(37+273)}\) kg.
As the weight of water vapor is in grams and the weight of air containing no water vapor is in kg, one needs to alter one so that they are in the same unit of measure. \(40\)g is equal to \(\frac{40}{1000}\)kg
To find the what percent the weight of water vapor in 1\(m^3\) of air at its saturation point is of the weight of 1\(m^3\) of air containing no water vapor one will go:
What's the significance of the term '1m3' in the question? That confused me a bit
Nidzo
1.)
At 37°C the weight of water vapor in \(1m^3\) is around \(40\)g of absolute humidity.
At 37°C the weight of air containing no water vapor is \(\frac{10^5}{287(37+273)}\) kg.
As the weight of water vapor is in grams and the weight of air containing no water vapor is in kg, one needs to alter one so that they are in the same unit of measure. \(40\)g is equal to \(\frac{40}{1000}\)kg
To find the what percent the weight of water vapor in 1\(m^3\) of air at its saturation point is of the weight of 1\(m^3\) of air containing no water vapor one will go:
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