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
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
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F239db1bd-bca7-46b2-879b-9072f95b41a3%2F09ec5e9d-f6f8-4d76-ae2c-bc50b3bd378a%2F3ghe2t_processed.jpeg&w=3840&q=75)
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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