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

Answer:

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"#.