As 390 g of hot milk cools in a mug, it transfers 30,000 j of heat to the environment. what is the temperature change of the milk? the specific heat of milk is 3.9 j/g•°c. show your work.

The correct answer is 19.72 °C. The first step is to determine the amount of heat that was lost per gram (30,000 J) / (390 g) = 76.92 J/g. Then to determine the temperature change, divide 76.92 J/g with the given specific heat of milk (76.92 J/g) / (3.9 J/g°C) = 19.72 °C.

The formula for calculating heat is Q=mCpdT
Q means the heat loss, m is for the mass, Cp is for the specific heat, dT is for the temperature change.

Since we are asked for the temperature change of the milk than we are going to find dT. Substituting the given to the equation:
30000 J=(390 g)*(3.9 J/g-C)*dT
dT= 19.72 C

Therefore, the temperature change of the milk is 19.72 degrees Celsius.