# 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?

## ${c}_{m i l k} = 3.9 J$/g°C

Jun 14, 2018

The temperature of the milk in the mug will decrease by $\approx {20}^{\circ} \text{C}$.

#### Explanation:

Use the following formula:

$q = m {c}_{p} \Delta T$,

where:

$q$ is heat energy, $m$ is mass, ${c}_{p}$ is specific heat capacity, and $\Delta T$ is the change in temperature.

Known

$q = \text{30000 J}$

$m = \text{390 g}$

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

Unknown

$\Delta T$

Solution

Rearrange the formula to isolate $\Delta T$. Plug in the known values and solve.

$\Delta T = \frac{q}{m \cdot {c}_{p}}$

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 $\approx {20}^{\circ} \text{C}$.