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The “steam” above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 250 g of hot coffee initially at $90.0^{\circ} \mathrm{C}$ if 2.00 g evaporates from it? The coffee is in a Styrofoam cup, so other methods of heat transfer can be neglected.

The final temperature will be $90-4.3=85.7^{\circ} \mathrm{C}$

Physics 101 Mechanics

Chapter 14

Heat and Heat Transfer Methods

Thermal Properties of Matter

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

Lectures

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So let's see what's exactly happening. Coffee is losing the temperature, whereas it is losing it by means off evaporation. So so there is a final temperature from ignition temperature, so massive coffee times, the specifications of copy times, the change in temperature. We don't know the final temperatures of let's write T F. Initial temperature is 90 on dhe, which is equal to mass off. Water evaporated on latent heat off vaporization. So let's now substitute all the values we have. So latent heat of vaporization of water is 2256 Killer June spoke ill of that. So massive water evaporated. Waas two guns. So let's do it this two times 10 power negativity times 2256 Science tempo A negative sort of positive. Three. Because it's killing Jews per kilogram. We must convert it to juice. Massive coffee. After after we lose two grams of water, massive coffee will be to 48 grafts to 48 times 10 Power three Negative three to convert it to kilograms specifications. Water is for 186 and we don't know TF yet, So let's do this. Calculations divide this whole quantity by this will get so we can just simply cancel these two terms. As you can see, it's a two foot two times 2256000 Divided by 2 48 divided by 4186 will be. So that gives me 4.34 62 Now there is one catch we cannot ignore. That is, they should be negative because this is the heat we lost. Because if you keep this positive, you will add 19 and four, which is against the common sense, because we are supposed to lose heat so supposed to decrease the temperature. So in this case, dancer will be t f is equal to 90 minus 4.34 or 35 approximately. So if you do this calculation, you will find that the answer is 86.65 degrees Celsius. Final temperature will be, um, decreased. Oh, sorry. This should be 85. Yes. So final temperature will be 85.7 degrees Celsius because we want answered in just three significant digits. Thank you.

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