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How many grams of coffee must evaporate from 350 g of coffee in a 100-g glass cup to cool the coffee from $95.0^{\circ} \mathrm{C}$ to $45.0^{\circ} \mathrm{C}$? You may assume the coffee has the same thermal properties as water and that the average heat of vaporization is 2340 kJ/kg (560 cal/g). (You may neglect the change in mass of the coffee as it cools, which will give you an answer that is slightly larger than correct.)

33.10042735 $\mathrm{g}$

Physics 101 Mechanics

Chapter 14

Heat and Heat Transfer Methods

Thermal Properties of Matter

University of Washington

Simon Fraser University

University of Sheffield

Lectures

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04:46

A thermos contains 150 ${c…

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A coffee cup calorimeter i…

01:59

The heat of vaporization o…

04:18

Heat of Vaporization How m…

Your 300 mL cup of coffee …

03:10

02:05

A coffee-cup calorimeter i…

so to solve this question, we need to first find what a question one must use, so we must use the question off. Q. Equal to mass times latent heat off vaporization. This is where you'll find them as from, but we don't know. Value of Q. It, uh, that can be found by using the fact that vaporizing this amount of coffee reduces the coffee's temperature overall, plus the glasses temperature by 15 to the senses. That is 95 to 45 So that must be emcee Delta T off glass plus M. C. Delta T off coffee. So we need to quit these two quantities to find this value. The mass now will be equal to M G C G plus M. C. See subsea times Delta T divided by off vaporization. So let's substitute on the values Mass is equal to M G, which is glass 0.1. Glass has specific it off. 8 40 Jules Tuberculosis pedigree Celsius. Plus we need to write the mass off coffee, which is 3 50 times. Specifications it Now we will assume it's full. 186 Same as water on change in temperature, as we know is 53 Celsius, divided by the Layton's Heat, which is 32340 kilo. Jules, it's a two thing for zero times 10 Power three Killer Jules per kilograms. Let's calculate this 0.1 times 8 40 plus 3 50 times. Okay, let me put it this year this should be 0.3 53 50 because it's in terms of crimes. So for 186 I went to about 15 divided by 2340 So the answer here is 33.1 times 10 power negative, three kilos. So this is 33.1 God. So we need to up evaporate this much amount of coffee to reduce the temperature to 45 degrees. This answer is slightly larger, because why we used this equation here? These values here, especially here 0.3 50. We know that this mass of coffee is decreasing when this is evaporating. So final mass of coffee is less than 0.35 which is approximately 0.317 That's the final mass of coffee, so but that is quite small compared to 3 50 33 So compared to 3 50 33 small, which is approximately 10% off a value. So our answer will not be ways different. It will be larger, but not much. Thank you.

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