College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question:**
Some carbon dioxide occupies 34.5 L at 49.0 °C. At what temperature will it occupy 56.2 L?
**Explanation:**
This question involves the principles of gas laws, specifically Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is held constant. To solve this problem, use the formula:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 = 34.5 \, \text{L} \) (initial volume)
- \( T_1 = 49.0 \, \text{°C} = 322.15 \, \text{K} \) (initial temperature in Kelvin, convert by adding 273.15)
- \( V_2 = 56.2 \, \text{L} \) (final volume)
- \( T_2 \) is the final temperature in Kelvin, which we need to find
Rearrange the formula to solve for \( T_2 \):
\[ T_2 = \frac{V_2 \times T_1}{V_1} \]
Calculate \( T_2 \) and convert back to Celsius if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc463f08e-ec7e-4810-a9a2-5563bca4d00b%2Fb157f084-b6e5-4d45-b7c0-b6f26e9d4f25%2Fa7lu5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Some carbon dioxide occupies 34.5 L at 49.0 °C. At what temperature will it occupy 56.2 L?
**Explanation:**
This question involves the principles of gas laws, specifically Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is held constant. To solve this problem, use the formula:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 = 34.5 \, \text{L} \) (initial volume)
- \( T_1 = 49.0 \, \text{°C} = 322.15 \, \text{K} \) (initial temperature in Kelvin, convert by adding 273.15)
- \( V_2 = 56.2 \, \text{L} \) (final volume)
- \( T_2 \) is the final temperature in Kelvin, which we need to find
Rearrange the formula to solve for \( T_2 \):
\[ T_2 = \frac{V_2 \times T_1}{V_1} \]
Calculate \( T_2 \) and convert back to Celsius if needed.
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