As 390-g of hot milk cools in a mug, it transfers 30,000 J of heat to the environment. How does the temperature of the milk change?

c_(milk)= 3.9 J/g°C

1 Answer
Jun 14, 2018

The temperature of the milk in the mug will decrease by ~~20^@"C".

Explanation:

Use the following formula:

q=mc_pDeltaT,

where:

q is heat energy, m is mass, c_p is specific heat capacity, and DeltaT is the change in temperature.

Known

q="30000 J"

m="390 g"

c_"milk"=("3.9 J")/("g"*""^@"C")

Unknown

DeltaT

Solution

Rearrange the formula to isolate DeltaT. Plug in the known values and solve.

DeltaT=q/(m*c_p)

DeltaT=(30000color(red)cancel(color(black)("J")))/((390color(red)cancel(color(black)("g")))xx((3.9color(red)cancel(color(black)("J")))/(color(red)cancel(color(black)("g"))*""^@"C")))="20"^@"C" (rounded to one significant figure)

The temperature of the milk in the mug will decrease by ~~20^@"C".