Calculate the energy required to heat 0.30 kg of water from 48.2 °c to 54.9 °C. Assume the specific heat capacity of water under these conditions is 4.18 J-gK. Round your answer to 2 significant digits. do
Calculate the energy required to heat 0.30 kg of water from 48.2 °c to 54.9 °C. Assume the specific heat capacity of water under these conditions is 4.18 J-gK. Round your answer to 2 significant digits. do
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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![### Calculating the Energy Required to Heat Water
**Problem Statement:**
Calculate the energy required to heat 0.30 kg of water from 48.2 °C to 54.9 °C. Assume the specific heat capacity of water under these conditions is 4.18 J·g⁻¹·K⁻¹. Round your answer to 2 significant digits.
1. **Mass of water (m):** 0.30 kg
2. **Initial temperature (T₁):** 48.2 °C
3. **Final temperature (T₂):** 54.9 °C
4. **Specific heat capacity of water (c):** 4.18 J·g⁻¹·K⁻¹
**Conversion of mass from kg to g:**
\[ \text{Mass} = 0.30 \, \text{kg} = 0.30 \times 1000 \, \text{g} = 300 \, \text{g} \]
**Temperature change (ΔT):**
\[ \Delta T = T₂ - T₁ = 54.9 \, \text{°C} - 48.2 \, \text{°C} = 6.7 \, \text{°C} \]
**Energy required (q):**
\[ q = m \cdot c \cdot \Delta T \]
\[ q = 300 \, \text{g} \times 4.18 \, \text{J·g⁻¹·K⁻¹} \times 6.7 \, \text{K} \]
Calculate the energy:
\[ q = 300 \times 4.18 \times 6.7 \]
\[ q = 8418.6 \, \text{J} \]
**Rounded to 2 significant digits:**
\[ q = 8400 \, \text{J} \]
### Explanation of Diagrams and Symbols
In the image above, there are placeholders for entering numerical values and symbols such as multiplication (×), division (÷), or others commonly used in mathematical equations.
- **Box with blue border:** This signifies where you input your numerical answer.
- **Symbol toolbox:** Contains various mathematical symbols and functions that may be used in solving the problem.
Here we have used the specific heat formula for calculating the energy](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91d4d95b-0585-4598-b79f-be9cda91865b%2F4807233c-1c3b-4807-bf3e-12a8ef77fcc3%2F5hwqy8u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Energy Required to Heat Water
**Problem Statement:**
Calculate the energy required to heat 0.30 kg of water from 48.2 °C to 54.9 °C. Assume the specific heat capacity of water under these conditions is 4.18 J·g⁻¹·K⁻¹. Round your answer to 2 significant digits.
1. **Mass of water (m):** 0.30 kg
2. **Initial temperature (T₁):** 48.2 °C
3. **Final temperature (T₂):** 54.9 °C
4. **Specific heat capacity of water (c):** 4.18 J·g⁻¹·K⁻¹
**Conversion of mass from kg to g:**
\[ \text{Mass} = 0.30 \, \text{kg} = 0.30 \times 1000 \, \text{g} = 300 \, \text{g} \]
**Temperature change (ΔT):**
\[ \Delta T = T₂ - T₁ = 54.9 \, \text{°C} - 48.2 \, \text{°C} = 6.7 \, \text{°C} \]
**Energy required (q):**
\[ q = m \cdot c \cdot \Delta T \]
\[ q = 300 \, \text{g} \times 4.18 \, \text{J·g⁻¹·K⁻¹} \times 6.7 \, \text{K} \]
Calculate the energy:
\[ q = 300 \times 4.18 \times 6.7 \]
\[ q = 8418.6 \, \text{J} \]
**Rounded to 2 significant digits:**
\[ q = 8400 \, \text{J} \]
### Explanation of Diagrams and Symbols
In the image above, there are placeholders for entering numerical values and symbols such as multiplication (×), division (÷), or others commonly used in mathematical equations.
- **Box with blue border:** This signifies where you input your numerical answer.
- **Symbol toolbox:** Contains various mathematical symbols and functions that may be used in solving the problem.
Here we have used the specific heat formula for calculating the energy
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