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(II) If the humidity is 45$\%$ at $30.0^{\circ} \mathrm{C},$ what is the dew point? Use linear interpolation to find the temperature of the dew point to the nearest degree.

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$16.6^{\circ} C$

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

Cornell University

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

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So we're doing Chapter 18 Problem 37. So it says if the humidity is that 45% a. T equaling 30 degrees Celsius, what is the dew point? And it says use linear interpretation on the temperature of the dew point. Here's degree. So first we need the saturated vapour pressure of water at 30 degrees Celsius and at 30 degrees Celsius we can look at table 18.2 on page 5 62 and we shouldn't see that this corresponds to bay piece at equaling 4240 Pascal's Okay, so we're gonna use it out. We also know that the relative humidity or a trail, as I call it, is given as p partial over peace at. And this then is Oh, so we're trying to figure out the dew point so we actually need this partial pressure so we can be arranged this equation soon. P partial is peace at times atrial. So this is 4240 times. The report for five replied that in this is 19 0 a. Pascal's. So now that we know the partial pressure here, we know also should know that the dew point do you Point is the temperature at which the partial crusher is the saturated vapour pressure. So we need to find what what t is peace at equaling 1908 Pascal's so from the table, we probably don't know the exact We don't have an exact value for the peace at, so we should see the two closest values ar 15 degrees we have. What is it? Uh, 17. 10 past cows and at 20 degrees there is 2 33 0 pastors. So to figure out the temperature for 1920 Pascal's we need to use linear interpellation here, and to do that is we take the temperature before the closest step before it, which we have 15. So this is temperature at 7 10 Pascal's 17 10 Pascal's. Then we add on are Sloped factor, which is 19 away minus 17. 10 Pascoe over 23 30 minus 17 10. Paschal's So this is the difference in Pascal's here, and we need to multiply this pi times the difference in temperatures, which is five degrees from 15 to 20 and this easily comes out to being 15 degrees Celsius close 1.6 degrees Celsius or 16.6 degrees Celsius. Awesome

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