Cooling a cup of tea with ice.

In summary, the problem involves bringing a 200 gram cup of boiling hot tea down to 65°C by adding ice initially at -15°C. The specific heat capacity of ice is 0.5 cal/g°C and the ice needs to absorb 7000 calories of heat. Using the formula for heat capacity, we can calculate that the mass of ice needed is approximately 45.9 grams. The 80 calories from the latent heat of melting ice are also taken into account.
  • #1
cragar
2,552
3

Homework Statement


your 200 gram cup of tea is boiling hot. About how much ice should you add to bring it down to 65C? Ice is initially at -15C. The specific heat capacity of ice id .5cal/gC

The Attempt at a Solution


So the ice we add needs to absorb 7000 calories of heat.
Heat capacity is Q/T heat divided by change in temperature . And specific heat capacity is is heat capacity divided by mass.
So to heat the ice to 0 Celsius we have
15C(.5cal)/gC(x) + 65(x) + 80 cal/g(x) =7000 calories.
cleaning it up
(15)(.5)x+65x+80x=7000 in units of energy
the 80 comes from the latent heat for melting ice which is 80cal/gram
and x is the unknown mass of ice.
and i get that x=45.9 grams of ice.
 
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  • #2
It looks correct.

ehild
 

Related to Cooling a cup of tea with ice.

1. How does adding ice to a cup of tea cool it down?

Ice cools a cup of tea down through a process known as heat transfer. When placed in the tea, the ice absorbs heat from the hot tea, causing it to melt and lower the overall temperature of the tea.

2. How long does it take for ice to cool a cup of tea?

The time it takes for ice to cool a cup of tea depends on various factors such as the temperature of the tea, the amount of ice used, and the size and material of the cup. Generally, it can take anywhere from 1-3 minutes for the tea to cool down to a drinkable temperature.

3. Can I use any type of ice to cool my tea?

Yes, you can use any type of ice to cool your tea, whether it be cubed, crushed, or shaved ice. However, crushed or shaved ice will cool the tea faster as they have a larger surface area in contact with the hot tea.

4. How can I cool my tea without diluting it?

If you want to cool your tea without diluting it, you can use larger ice cubes. This will slow down the melting process and keep your tea from becoming too watered down. You can also try using frozen fruit or tea cubes made from the same type of tea to cool it down without diluting it.

5. Is it safe to drink tea with ice?

Yes, it is safe to drink tea with ice. As long as the ice is made from clean, potable water, it will not pose any health risks. However, if you are concerned about bacteria, you can use boiled or filtered water to make your ice cubes.

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