Some carbon dioxide occupies 34.5 L at 49.0 °C. At what temperature will it occupy 56.2 L?

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.
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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