suppose you and a friend are making iced tea using identical glasses. You both use the same amount of water, and the water temperature is the same in both glasses. Explain how you can tell who added more ice tea mix to the glass.

Iced-Tea Problem

220 g of 35˚C tea (water) is poured over 250 g of -10˚C ice.

What happens...

The warm water (tea) will cool down to 0˚C. As it cools the ice will heat up to 0˚C and then start to melt.

There is plenty of ice however and only a portion of it will melt. Find the amount of ice that melts into water

and you’ll know the final composition and even the dilution factor on the tea.

Cool tea water down to 0˚C

4.184 J/g˚C · 220 g · 35˚C = 32216.8 J removed to cool tea to 0˚C

Warm ice up to 0˚C

2.09 J/g˚C · 250 g · 10˚C = 5225 J to heat ice up to 0˚C

This heat comes from the cooling water, so substract this amount off the total above

32216.8 - 5225 = 26991.8 J of heat that will MELT the ice

mass of ice melted = 26991.8 / 334 = 80.8 g of ice melted

220 g + 80.8 = 300.8 g of water

250 g - 80.8 = 169.2 g of ice

final mixture for

my glass of iced

tea all at 0˚C

220.0 g original tea

300.8 g final tea

The dilution factor is simply the original volume

over the final volume (or masses here ). = .731 or 73.1%

of the original

concentration

If I’m going to get a dilution of 73.1%, I should

compensate by mixing my tea in 26.9% LESS

volume than the directions state. So I will not dilute

the tea to 2 quarts (64 oz), but rather to 1.462

quarts (46.8 oz).

It’s hot and I want a glass of iced tea as soon as possible. The directions for my tea say to boil some water,

add 2 tea bags (these are the big bags), steep for 4-5 minutes, then add enough water to make 2 quarts which

turns out to be a pitcher of tea. However, if I make this tea the exact concentration I want now, when I pour

it over ice the ice will melt (because the tea will still be quite warm) and my tea will be too dilute. So I

calculate how much stronger I should make the tea KNOWING I will pour the warm tea over ice to make

my glass of iced tea.

(a). What is the final temperature and composition of the glass of iced-tea?

(b). What will be the concentration of the tea relative to the original concentration?

(c). How concentrated should I mix the tea knowing that it will be diluted when

poured over the ice?

(a)

(c)

(b)

only 73.1% of the full

amount to compensate

for dilution

c

explanation:

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