An Insulated Thermos contains a volume V of hot coffee at temperature T. You put

Question

An Insulated Thermos contains a volume V of hot coffee at temperature T. You put in an ice cube with mass m at its melting point to cool the coffee. What is the temperature of the contents of your thermos once the ice cube has melted? Treat the coffee as though it were pure water and neglected energy exchanges with the environment. (Use any variables or symbol stated above along with the following as necessary: c for the specific heat of water, L, for the latent heat of fusion of water, and p for the density of water)

Explanation / Answer

Heat gained by coffee = Heat lost by ice cube

mcoffeeccoffeeT = miceLice                                                                        (L=latent heat of fusion)

mwatercwaterT = miceLice    

mwatercwater(Tf –Ti) = miceLice    

but water = mwater/Vwater      => mwater = water*Vwater      

Hence,

water*Vwater cwater(Tf –Ti) = miceLice    

(Tf –Ti) = (miceLice )/(water*Vwater cwater)

Note that since Tf < Ti , T will be negative thus -T = -(Tf –Ti)

So,

-(Tf –Ti) = (miceLice )/(water*Vwater cwater)

(Tf –Ti) = -[ (miceLice )/(water*Vwater cwater)]

Tf = - [(miceLice )/(water*Vwater cwater)] + Ti

but Ti =T

Tf = - [(miceLice )/(water*Vwater cwater)] + T

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