1. People buying food in sealed bags at high elevation often notice that the bags are puffed up because the air inside has expanded. A bag of pretzels was packed at a pressure of 1.00 atm and a temperature of 22.0 °C. When opened at a summer picnic in Santa Fe, New Mexico, at a temperature of 32.0 °C, the volume of air in the bag is 1.19 times its original volume. What is the pressure of the air P Santa Fe ? P Santa Fe ✔atm
1. People buying food in sealed bags at high elevation often notice that the bags are puffed up because the air inside has expanded. A bag of pretzels was packed at a pressure of 1.00 atm and a temperature of 22.0 °C. When opened at a summer picnic in Santa Fe, New Mexico, at a temperature of 32.0 °C, the volume of air in the bag is 1.19 times its original volume. What is the pressure of the air P Santa Fe ? P Santa Fe ✔atm
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![### Air Expansion in Food Packaging Due to Elevation Changes
1. **Observing Changes in Packaged Food at High Elevation:**
People buying food in sealed bags at high elevation often notice that the bags are puffed up because the air inside has expanded. Consider a scenario where:
- A bag of pretzels was initially packed at a sea-level pressure of 1.00 atm and a temperature of 22.0 °C.
- At a summer picnic in Santa Fe, New Mexico, with an ambient temperature of 32.0 °C, the volume of air in the bag is observed to be 1.19 times its original volume.
The question posed is: What is the pressure of the air \( P_{\text{Santa Fe}} \)?
This can be calculated using the ideal gas law principle, adjusting for temperature and volume changes, recognizing that temperature must be in kelvin for accurate calculation.
2. **Calculation Section:**
- Convert temperatures from Celsius to Kelvin:
- Initial temperature \( T_1 \): \( 22.0 \,°C = 295.15 \, K \)
- Final temperature \( T_2 \): \( 32.0 \,°C = 305.15 \, K \)
- Apply the combined gas law: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)
- Where:
- \( P_1 = 1.00 \, atm \)
- \( V_1 = 1 \) (initial volume)
- \( V_2 = 1.19 \, V_1 \) (final volume)
- \( T_1 = 295.15 \, K \)
- \( T_2 = 305.15 \, K \)
- Rearrange and solve for \( P_2 \) (Pressure in Santa Fe):
\[ P_{\text{Santa Fe}} = \frac{P_1 \cdot V_1 \cdot T_2}{V_2 \cdot T_1} = \frac{1.00 \cdot 1 \cdot 305.15}{1.19 \cdot 295.15} \]
\[ P_{\text{Santa Fe}} \approx 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0761ca0b-8a30-47ed-b77e-00687bf0302e%2F08ea6e3e-055e-4489-81b8-194f4ef1e46b%2Fd2hfh7v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Air Expansion in Food Packaging Due to Elevation Changes
1. **Observing Changes in Packaged Food at High Elevation:**
People buying food in sealed bags at high elevation often notice that the bags are puffed up because the air inside has expanded. Consider a scenario where:
- A bag of pretzels was initially packed at a sea-level pressure of 1.00 atm and a temperature of 22.0 °C.
- At a summer picnic in Santa Fe, New Mexico, with an ambient temperature of 32.0 °C, the volume of air in the bag is observed to be 1.19 times its original volume.
The question posed is: What is the pressure of the air \( P_{\text{Santa Fe}} \)?
This can be calculated using the ideal gas law principle, adjusting for temperature and volume changes, recognizing that temperature must be in kelvin for accurate calculation.
2. **Calculation Section:**
- Convert temperatures from Celsius to Kelvin:
- Initial temperature \( T_1 \): \( 22.0 \,°C = 295.15 \, K \)
- Final temperature \( T_2 \): \( 32.0 \,°C = 305.15 \, K \)
- Apply the combined gas law: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)
- Where:
- \( P_1 = 1.00 \, atm \)
- \( V_1 = 1 \) (initial volume)
- \( V_2 = 1.19 \, V_1 \) (final volume)
- \( T_1 = 295.15 \, K \)
- \( T_2 = 305.15 \, K \)
- Rearrange and solve for \( P_2 \) (Pressure in Santa Fe):
\[ P_{\text{Santa Fe}} = \frac{P_1 \cdot V_1 \cdot T_2}{V_2 \cdot T_1} = \frac{1.00 \cdot 1 \cdot 305.15}{1.19 \cdot 295.15} \]
\[ P_{\text{Santa Fe}} \approx 0
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