Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Question
**Problem Statement:** If a system has 375 kcal of work done to it, and releases \(5.00 \times 10^2\) kJ of heat into its surroundings, what is the change in internal energy (\(\Delta E\) or \(\Delta U\)) of the system? **Solution:** To find the change in internal energy (\(\Delta E\)), we use the first law of thermodynamics, which states: \[ \Delta E = q + w \] Where: - \(q\) is the heat exchanged by the system. - \(w\) is the work done on the system. **Given Values:** - Work done on the system: \(w = 375 \text{ kcal}\) - Heat released into surroundings: \(q = -500 \text{ kJ}\) **Conversion:** 1 kcal = 4.184 kJ Thus, converting work from kcal to kJ: \[ 375 \text{ kcal} \times 4.184 \frac{\text{kJ}}{\text{kcal}} = 1569 \text{ kJ} \] Now, substitute the values into the formula: \[ \Delta E = -500 \text{ kJ} + 1569 \text{ kJ} = 1069 \text{ kJ} \] **Conclusion:** The change in internal energy (\(\Delta E\)) of the system is 1069 kJ.
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Transcribed Image Text:**Problem Statement:** If a system has 375 kcal of work done to it, and releases \(5.00 \times 10^2\) kJ of heat into its surroundings, what is the change in internal energy (\(\Delta E\) or \(\Delta U\)) of the system? **Solution:** To find the change in internal energy (\(\Delta E\)), we use the first law of thermodynamics, which states: \[ \Delta E = q + w \] Where: - \(q\) is the heat exchanged by the system. - \(w\) is the work done on the system. **Given Values:** - Work done on the system: \(w = 375 \text{ kcal}\) - Heat released into surroundings: \(q = -500 \text{ kJ}\) **Conversion:** 1 kcal = 4.184 kJ Thus, converting work from kcal to kJ: \[ 375 \text{ kcal} \times 4.184 \frac{\text{kJ}}{\text{kcal}} = 1569 \text{ kJ} \] Now, substitute the values into the formula: \[ \Delta E = -500 \text{ kJ} + 1569 \text{ kJ} = 1069 \text{ kJ} \] **Conclusion:** The change in internal energy (\(\Delta E\)) of the system is 1069 kJ.
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