The total volume of the Pacific Ocean is estimated to be 7.20 x 108 km³. A medium-sized atomic bomb produces 1.00 × 105 J of energy upon explosion. Calculate the number of atomic bombs needed to release enough energy to raise the temperature of the water in the Pacific Ocean by 2.000°C. Assume the density of sea water to be 1.00 g/mL. Enter your answer in scientific notation. x 10

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### Energy Calculation in the Pacific Ocean

#### Problem Statement:
The total volume of the Pacific Ocean is estimated to be \( 7.20 \times 10^8 \, \text{km}^3 \). A medium-sized atomic bomb produces \( 1.00 \times 10^{15} \) J (joules) of energy upon explosion. Calculate the number of atomic bombs needed to release enough energy to raise the temperature of the water in the Pacific Ocean by \( 2.00^\circ C \). 

Assume that:
- The density of seawater is \( 1.00 \, \text{g/mL} \).
- Provide your answer in scientific notation.

#### Answer Box:
\[
\boxed{ \times 10^ }
\]

#### Procedure to Calculate:
1. **Convert the volume of the Pacific Ocean to cubic meters:**
   - Volume metric conversion: \( 1 \, \text{km}^3 = 1 \times 10^9 \, \text{m}^3 \)
   - Pacific Ocean volume: \( 7.20 \times 10^8 \, \text{km}^3 \times 1 \times 10^9 \, \text{m}^3/\text{km}^3 = 7.20 \times 10^{17} \, \text{m}^3 \)

2. **Convert the volume to grams:**
   - Using the density of seawater (1 g/mL), recognize that \( 1 \text{m}^3 = 1 \times 10^6 \, \text{mL} \)
   - Therefore, \( 7.20 \times 10^{17} \, \text{m}^3 \times 1 \times 10^6 \, \text{g}/\text{m}^3 = 7.20 \times 10^{23} \, \text{g} \)

3. **Calculate the energy required to raise the temperature:**
   - Specific heat capacity of water = \( 4.186 \, \text{J/g} \cdot \text{°C} \)
   - Temperature change = \( 2.00^\circ C \)
   - Total energy required = mass \(\times\) specific heat \(\times\) temperature change
Transcribed Image Text:### Energy Calculation in the Pacific Ocean #### Problem Statement: The total volume of the Pacific Ocean is estimated to be \( 7.20 \times 10^8 \, \text{km}^3 \). A medium-sized atomic bomb produces \( 1.00 \times 10^{15} \) J (joules) of energy upon explosion. Calculate the number of atomic bombs needed to release enough energy to raise the temperature of the water in the Pacific Ocean by \( 2.00^\circ C \). Assume that: - The density of seawater is \( 1.00 \, \text{g/mL} \). - Provide your answer in scientific notation. #### Answer Box: \[ \boxed{ \times 10^ } \] #### Procedure to Calculate: 1. **Convert the volume of the Pacific Ocean to cubic meters:** - Volume metric conversion: \( 1 \, \text{km}^3 = 1 \times 10^9 \, \text{m}^3 \) - Pacific Ocean volume: \( 7.20 \times 10^8 \, \text{km}^3 \times 1 \times 10^9 \, \text{m}^3/\text{km}^3 = 7.20 \times 10^{17} \, \text{m}^3 \) 2. **Convert the volume to grams:** - Using the density of seawater (1 g/mL), recognize that \( 1 \text{m}^3 = 1 \times 10^6 \, \text{mL} \) - Therefore, \( 7.20 \times 10^{17} \, \text{m}^3 \times 1 \times 10^6 \, \text{g}/\text{m}^3 = 7.20 \times 10^{23} \, \text{g} \) 3. **Calculate the energy required to raise the temperature:** - Specific heat capacity of water = \( 4.186 \, \text{J/g} \cdot \text{°C} \) - Temperature change = \( 2.00^\circ C \) - Total energy required = mass \(\times\) specific heat \(\times\) temperature change
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