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How many milliliters of water a $23^{\circ} \mathrm{C}$ with a density of 1.00 $\mathrm{g} / \mathrm{mL}$ mixed with 180 $\mathrm{mL}$ (about 6 $\mathrm{oz} )$ of coffee at $95^{\circ} \mathrm{C}$ so that the resulting combination will have a temperature of $60^{\circ} \mathrm{C} ?$ Assume that coffee and water have the same density and the same specific heat.

$V_{\mathrm{H}_{2} \mathrm{O}}=170 \mathrm{mL}$

01:34

Aadit S.

Chemistry 101

Chapter 5

Thermochemistry

Drexel University

University of Toronto

Lectures

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calculate how many millions of water The temperature of 23°C.. and those day one must be mixed with 180 of coffee at 95°C to have a temperature of 60 degrees overall. So the mass of the coffee heat capacity of the coffee and we felt that he coffee is equal to mm mass of the water heat capacity of the water change in temperature of the water. So we can replace the mass here. Uh we know that density is equal to mass times volume. Or is there a mass over volume? So mass is equal to density times the volume. Mhm. And so we can have um the density of the coffee, the volume of the coffee. That was a key capacity of the coffee changing temperature. The coffee because of the mass of sorry, the density of the water, um volume of the water capacity, build water felt. Key of the water. And in this question we're told that we are to assume that the coffee and water have the same density and the same specific heat. So if they have the same density and the same specific heat, you can cancel that out. And we have the volume of the coffee delta. T. Of the coffee secret of the volume of the water delta. T. Of the water. And we know that the volume of the coffee is 180. The temperature of the coffee Starts off at 95°C.. Her final temperature here Is 60°C -95°C.. Right, That was going to 60. Final medicine Would be the other way around Delta T. Here would be 95°C -60°C.. And this would be called to the volume of the water. And the water is Uh 60°C and initially 23°C.. So, solving for the volume of the water, we find that this is equal to Mhm. Yeah, I just 170 .27 ml of this would be the volume of the water that would be needed.

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