A hot air balloon is filled with 1.11 × 106 L of an ideal gas on a cool morning (11 °C). The air is heated to 119 °C. What is the volume of the air in the balloon after it is heated? Assume that none of the gas escapes from the balloon. volume: L
A hot air balloon is filled with 1.11 × 106 L of an ideal gas on a cool morning (11 °C). The air is heated to 119 °C. What is the volume of the air in the balloon after it is heated? Assume that none of the gas escapes from the balloon. volume: L
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![## Physics of Hot Air Balloons: Volume and Temperature Relationship
### Problem Statement:
A hot air balloon is initially filled with \(1.11 \times 10^6\) L of an ideal gas on a cool morning when the temperature is 11°C. The air inside the balloon is then heated to 119°C. You are tasked with determining the volume of the air in the balloon after it has been heated, assuming that no gas escapes from the balloon.
### Input and Output:
- Initial volume of the balloon at 11°C: \(1.11 \times 10^6\) L
- Initial temperature: 11°C
- Final temperature: 119°C
- Calculate the final volume of the balloon.
### Output Field:
- Volume: (This is where the calculated volume in liters will be entered)
### Additional Information:
This problem can be solved using the principles of the ideal gas law and the relationship of volume and temperature in gases, known as Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is constant.
### Calculation:
To find the new volume when the air is heated, use the formula:
\[ V_1/T_1 = V_2/T_2 \]
Where:
- \( V_1 \) is the initial volume.
- \( T_1 \) is the initial temperature in Kelvin.
- \( V_2 \) is the final volume.
- \( T_2 \) is the final temperature in Kelvin.
Convert temperatures from Celsius to Kelvin by adding 273.15. Then, solve for the final volume to fill in the field provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6797ee8f-35b0-45f9-be91-6b4961db7d8a%2F7ff861f6-349d-4cbb-858e-f797b2de2c07%2F1keeie8_processed.png&w=3840&q=75)
Transcribed Image Text:## Physics of Hot Air Balloons: Volume and Temperature Relationship
### Problem Statement:
A hot air balloon is initially filled with \(1.11 \times 10^6\) L of an ideal gas on a cool morning when the temperature is 11°C. The air inside the balloon is then heated to 119°C. You are tasked with determining the volume of the air in the balloon after it has been heated, assuming that no gas escapes from the balloon.
### Input and Output:
- Initial volume of the balloon at 11°C: \(1.11 \times 10^6\) L
- Initial temperature: 11°C
- Final temperature: 119°C
- Calculate the final volume of the balloon.
### Output Field:
- Volume: (This is where the calculated volume in liters will be entered)
### Additional Information:
This problem can be solved using the principles of the ideal gas law and the relationship of volume and temperature in gases, known as Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is constant.
### Calculation:
To find the new volume when the air is heated, use the formula:
\[ V_1/T_1 = V_2/T_2 \]
Where:
- \( V_1 \) is the initial volume.
- \( T_1 \) is the initial temperature in Kelvin.
- \( V_2 \) is the final volume.
- \( T_2 \) is the final temperature in Kelvin.
Convert temperatures from Celsius to Kelvin by adding 273.15. Then, solve for the final volume to fill in the field provided.
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