The temperature of the brewed tea is typically 96 C and I have to wait some time

Question

The temperature of the brewed tea is typically 96 C and I have to wait some time for it to cool down before I can drink it. Some days, I’m in a rush and don’t have the time to wait, so I put a few ice cubes in the cup to speed up the cooling process. How many ice cubes do I need to use to get the temperature of the tea down to 60 C? Assume a cup is equal to 8 ounces and that the ice cubes are initially at -7 C and weigh 11 g each. Use the following data: Specific heat of ice = 2.108 J/g K Specific heat of water = 4.184 J/g K

Explanation / Answer

1 ounce= 28. 35 gm, 8 ounces= 8* 28.35 gm =226.8 gm of tea

heat to be lost by tea = mass* specific heat of water* temperature difference= 226.8*4.184*(96-60)= 34162 joules

this heat has to come from ice cubes avilable at -7 deg.c. Let n= no of ice cubes

from -7 deg.c to 0 deg.c, ice gains sensible heat which is = n* 11* 2.108*7= 162.32n

at 0 deg.c ice becomes liquid water at 0 deg.c,by gaiming latent heat of fusion whose value is 333 J/gm. heat gained from latent heat= n*11*333 =363n

from 0 deg.c liquid water gains sensible heat which is = n*11*4.184*60=2761.44n

total heat taken by cubes= 162.32n+ 363n+2761.44n= 3287n= 34162

n= 10 cubes

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