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To solve this question, we’ll calculate the amount of energy required to cool down 15 bottles of beer from 15°C to 7°C.

### Given Data
- Number of bottles, \( n = 15 \)
- Initial temperature, \( T_{\text{initial}} = 15^\circ \text{C} \)
- Final temperature, \( T_{\text{final}} = 7^\circ \text{C} \)
- Volume per bottle, \( V = 30 \, \text{centiliters} = 0.3 \, \text{liters} = 0.0003 \, \text{m}^3 \) 
- Specific heat capacity, \( c = 4186 \, \frac{J}{kg \cdot K} \)
- Density of beer, \( \rho = 1000 \, \frac{kg}{m^3} \)

### Step 1: Calculate Mass of Beer in Each Bottle
Since density \( \rho = \frac{m}{V} \), we find mass \( m \) as:
\[
m = \rho \cdot V = 1000 \, \frac{kg}{m^3} \times 0.0003 \, m^3 = 0.3 \, \text{kg}
\]

### Step 2: Calculate the Total Mass for 15 Bottles
\[
\text{Total mass} = 15 \times 0.3 \, \text{kg} = 4.5 \, \text{kg}
\]

### Step 3: Calculate the Temperature Difference
\[
\Delta T = T_{\text{final}} - T_{\text{initial}} = 7 - 15 = -8 \, ^\circ \text{C} \, \text{(or } -8 \, K\text{)}
\]

### Step 4: Calculate the Energy Required
The energy required to change the temperature is given by the formula:
\[
Q = m \cdot c \cdot \Delta T
\]
Substitute in the values:
\[
Q = 4.5 \, \text{kg} \times 4186 \, \frac{J}{kg \cdot K} \times (-8 \, K)
\]
\[
Q = 4.5 \times 4186 \times -8 = -150,696 \, \text{J}
\]

Since we're only interested in the magnitude of energy (the absolute value), we can say:
\[
Q = 150,696 \, \text{J}
\]

### Answer
The energy required to cool the beer down to 7°C is **150,696 Joules**.

Would you like a detailed breakdown of each step, or do you have any questions?

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### Related Questions
1. How would the answer change if the specific heat capacity of beer was different?
2. What if we only had 10 bottles instead of 15? How would that affect the energy required?
3. How does the cooling energy change if we use bottles with a different volume, e.g., 50 centiliters?
4. How can we convert this energy into kilowatt-hours (kWh) to understand the power consumption better?
5. How would we calculate the energy if we cooled the beer in multiple stages, e.g., from 15°C to 10°C and then 10°C to 7°C?

### Quick Tip
Always keep track of units, especially when converting between liters, milliliters, kilograms, and grams, as errors in unit conversions are common in thermodynamics problems.

We zetten nu 15 biertjes in de koelkast, deze zijn allemaal 15 graden Celsius en hebben (glas en inhoud samen) een volume van 30 centiliter en een soortelijke warmte (c) van 4186 J/kg * K. Daarnaast mag er een dichtheid van 1000 kg/m^3 worden verondersteld. Hoeveel energie is er voor nodig om het bier op 7 graden Celsius te krijgen. (In Joules)

Learn how to calculate the energy required to cool 15 bottles of beer from 15°C to 7°C. This problem involves concepts of thermodynamics, including specific heat capacity and density. Suitable for students in Grades 10-12.

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