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? (cmilk = 3.9 J/g°C)


It decreases by 20°C.


It decreases by 77°C.


It increases by 20°C.


It increases by 77°C.

Answer 1

To find out how the temperature of the milk changes, we can use the formula relating heat transfer to mass, specific heat capacity, and temperature change:

\[
q = m \cdot c \cdot \Delta T
\]

where:
- \( q \) is the heat transferred (in joules),
- \( m \) is the mass (in grams),
- \( c \) is the specific heat capacity (in J/g°C),
- \( \Delta T \) is the change in temperature (in °C).

In this case:
- \( q = -30,000 \, J \) (the negative sign indicates that the milk is losing heat),
- \( m = 390 \, g \),
- \( c = 3.9 \, J/g°C \).

Now, we can rearrange the formula to solve for \( \Delta T \):

\[
\Delta T = \frac{q}{m \cdot c}
\]

Substituting the values in:

\[
\Delta T = \frac{-30,000 \, J}{390 \, g \cdot 3.9 \, J/g°C}
\]

Calculating the denominator:

\[
390 \cdot 3.9 = 1521
\]

Now calculate \( \Delta T \):

\[
\Delta T = \frac{-30,000}{1521} \approx -19.68 \, °C
\]

Since we round, we can say that:

\[
\Delta T \approx -20 \, °C
\]

Thus, the temperature of the milk decreases by about 20°C.

**The answer is: It decreases by 20°C.**