Some gas initially at 60°F is heated to 200°F at constant pressure. If the initial volume of the gas is 16 ft3, determine the final volume of the gas. 




To solve this problem, we can use **Charles's Law**, which describes how gases expand when heated at constant pressure. Charles's Law is given by the formula:

\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]

Where:
- \( V_1 \) = initial volume of the gas = 16 ft³,
- \( V_2 \) = final volume of the gas (what we are solving for),
- \( T_1 \) = initial temperature of the gas in Kelvin,
- \( T_2 \) = final temperature of the gas in Kelvin.

### Step 1: Convert the temperatures from Fahrenheit to Kelvin.
The formula to convert Fahrenheit to Kelvin is:

\[
T(K) = \frac{5}{9}(T(F) - 32) + 273.15
\]

For the initial temperature (\( T_1 \)) of 60°F:

\[
T_1(K) = \frac{5}{9}(60 - 32) + 273.15 = 288.71 \, K
\]

For the final temperature (\( T_2 \)) of 200°F:

\[
T_2(K) = \frac{5}{9}(200 - 32) + 273.15 = 366.48 \, K
\]

### Step 2: Apply Charles's Law.

Using the formula:

\[
\frac{16}{288.71} = \frac{V_2}{366.48}
\]

Now, solving for \( V_2 \):

\[
V_2 = \frac{16 \times 366.48}{288.71} \approx 20.3 \, \text{ft}^3
\]

### Final Answer:
The final volume of the gas is approximately **20.3 ft³**.

Let me know if you want more details, or have any questions!

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Here are some related questions:

1. What happens if the pressure is not constant during the heating process?
2. How would the volume change if the gas was cooled instead of heated?
3. What is the relationship between pressure and volume in gases?
4. Can Charles's Law be applied to liquids? Why or why not?
5. What are the assumptions of the ideal gas law?

**Tip:** Always convert temperatures to an absolute scale (Kelvin) when dealing with gas laws.

Some gas initially at 60°F is heated to 200°F at constant pressure. If the initial volume of the gas is 16 ft³, determine the final volume of the gas.

Learn how to determine the final volume of a gas heated from 60°F to 200°F at constant pressure using Charles's Law. This detailed solution involves converting temperatures from Fahrenheit to Kelvin and applying gas laws. Suitable for Grades 9-12.

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