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

Chemistry
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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
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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.
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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