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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![**Problem Statement:**
How much would the temperature of 295 g of water increase if 17.4 kJ of heat were added? (The specific heat of liquid water is: 4.184 J/g °C)
**Solution:**
To calculate the temperature increase (\(\Delta T\)) when a certain amount of heat (\(Q\)) is added to a given mass (\(m\)) of water, we can use the specific heat capacity formula:
\[ \Delta T = \frac{Q}{m \cdot c} \]
Where:
- \(Q\) is the heat added (in joules)
- \(m\) is the mass of the water (in grams)
- \(c\) is the specific heat capacity of the substance (for water, \(4.184 \, \text{J/g} \, ^\circ\text{C}\))
Given values:
- Mass of water (\(m\)): 295 g
- Heat added (\(Q\)): 17.4 kJ = 17,400 J (since 1 kJ = 1000 J)
- Specific heat capacity of water (\(c\)): 4.184 J/g °C
By substituting these values into the formula:
\[ \Delta T = \frac{17,400\, \text{J}}{295\, \text{g} \times 4.184\, \text{J/g} \, ^\circ\text{C}} \]
\[ \Delta T = \frac{17,400}{1233.28} \, ^\circ\text{C} \]
\[ \Delta T \approx 14.1 \, ^\circ\text{C} \]
So, the temperature of the 295 g of water would increase by approximately 14.1 °C if 17.4 kJ of heat were added.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35780925-5e45-4c26-92de-ecbbabfbfb48%2F16160ae4-5900-484b-9a09-77ef9dfd470a%2Fv60cue_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
How much would the temperature of 295 g of water increase if 17.4 kJ of heat were added? (The specific heat of liquid water is: 4.184 J/g °C)
**Solution:**
To calculate the temperature increase (\(\Delta T\)) when a certain amount of heat (\(Q\)) is added to a given mass (\(m\)) of water, we can use the specific heat capacity formula:
\[ \Delta T = \frac{Q}{m \cdot c} \]
Where:
- \(Q\) is the heat added (in joules)
- \(m\) is the mass of the water (in grams)
- \(c\) is the specific heat capacity of the substance (for water, \(4.184 \, \text{J/g} \, ^\circ\text{C}\))
Given values:
- Mass of water (\(m\)): 295 g
- Heat added (\(Q\)): 17.4 kJ = 17,400 J (since 1 kJ = 1000 J)
- Specific heat capacity of water (\(c\)): 4.184 J/g °C
By substituting these values into the formula:
\[ \Delta T = \frac{17,400\, \text{J}}{295\, \text{g} \times 4.184\, \text{J/g} \, ^\circ\text{C}} \]
\[ \Delta T = \frac{17,400}{1233.28} \, ^\circ\text{C} \]
\[ \Delta T \approx 14.1 \, ^\circ\text{C} \]
So, the temperature of the 295 g of water would increase by approximately 14.1 °C if 17.4 kJ of heat were added.
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