How Much Ice to Cool Boiling Tea to 65C?

[cragar]

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.

 

[ehild]

It looks correct.

ehild