Question

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`

Answer 1

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"`.