To make iced tea, you start by brewing the tea with hot water. Then you add ice. If you start with 1.0 L...?

Question

To make iced tea, you start by brewing the tea with hot water. Then you add ice. If you start with 1.0 L of 90.0º Celsius tea, what is the minimum amount of ice needed to cool it to 0º Celsius? Would it be better to let the tea cool to room temperature before adding the ice?

This problem is confusing me.
Please help me.

Answer 1

The specific heat of water is 1 cal/gram-deg C, or 4.1814 J/g-deg C Therefore, in order to cool 1.0 L (= 1000 ml, which would have a mass of 1000 g) from 90.0° C to 0° C, you would need to remove
(4.1814 J/g-deg C) * (1000 g) * (90° C - 0°C) = 376,326 J of heat.

The latent heat of melting of ice is 334 J/g. Therefore, in order to remove the required 376,326 J of heat, you would need
(376,326 J) / (334 J/g) = 1,127 g.

If you used this method to cool the tea, the required 1127 g of ice would melt to form 1127 ml = 1.127 L of water, more than the 1.0 L of water you started with. In other words, you'd dilute the tea by more than half. Pretty weak stuff. Better to let it cool on its own to room temp before adding the ice.

By the way, pay attention to significant figures here -- I haven't. You really shouldn't carry more than 2 throughout the calculations, which is the precision to which the least-precise given value id presented.

Answer 2

The liter of tea has to loose an amount Q of heat according to
Q = m*c*deltaT
where m is the mass of the tea
c is the specific heat of the tea
deltaT is the temp change: 90 degrees C

The ice that is added will melt to water at 0º Celsius. You don't say if the ice starts at 0º Celsius. That would be the simplest. Find the heat of fusion of ice and calculate how much ice is required for its total heat of fusion to equal the Q from above.

Answer 3

convey 5 cups of unpolluted chilly water to a "boil". Pour over 5 tea bags. Steep for 3 - 5 minutes. eliminate the tea bags and upload 3 - 5 cups of chilly water (looking on your determination of tea capability). Pour over ice in glass. upload sugar or sweetener and right with lemon.