How much energy must be transferred away from .5kg of 10 degrees Celsius milk in order for it to turn into ice cream? Assume the heat of fusion for milk is 2.8x10^5 J/kg. The specific heat for milk is 3930 J/kgC.

Explanation:

First of all, we have to calculate the amount of energy that must be transferred away from the milk in order to bring it to the freezing temperature, zero degrees. This is given by:

where:

m = 0.5 kg is the mass of milk

is the specific heat of milk

is the change in temperature

Substituting,

Then, after the milk has reached its freezing temperature, the amount of energy that must be removed in order to turn it into ice cream (convert it from liquid to solid) is given by:

where

m = 0.5 kg is the mass of milk

is the specific heat of fusion

Substituting,

Therefore, the total heat needed is

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west