To determine the final volume of the gas after heating, we can use Charles's Law, which states that for a given mass of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature (measured in Kelvin). Mathematically, this is expressed as:

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Where:

• $V_1$ = initial volume
• $T_1$ = initial absolute temperature (in Kelvin)
• $V_2$ = final volume
• $T_2$ = final absolute temperature (in Kelvin)

Step-by-step solution:

1. Convert the temperatures to Kelvin:

   • Temperature in Kelvin is obtained by adding 273.15 to the temperature in Fahrenheit (converted to Celsius).
   • First, convert the temperatures from Fahrenheit to Celsius: $T(°C) = \frac{5}{9} (T(°F) - 32)$
     • For $T_1 = 60°F$: $T_1(°C) = \frac{5}{9} (60 - 32) = \frac{5}{9} \times 28 = 15.56°C$
     • For $T_2 = 200°F$: $T_2(°C) = \frac{5}{9} (200 - 32) = \frac{5}{9} \times 168 = 93.33°C$

2. Convert Celsius to Kelvin:

   • $T_1(K) = 15.56 + 273.15 = 288.71K$
   • $T_2(K) = 93.33 + 273.15 = 366.48K$

3. Apply Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ Substitute the known values ($V_1 = 19 \, \text{ft}^3$, $T_1 = 288.71 \, K$, and $T_2 = 366.48 \, K$):

   $\frac{19}{288.71} = \frac{V_2}{366.48}$

4. Solve for $V_2$: $V_2 = \frac{19 \times 366.48}{288.71}$

Now let's calculate that:

$V_2 \approx \frac{19 \times 366.48}{288.71} = 24.12 \, \text{ft}^3$

Final Answer:

The final volume of the gas is approximately 24.12 ft³.

Would you like more details on any step? Here are some related questions:

1. How does Charles's Law apply to real-life gas expansion problems?
2. Can you explain the difference between Charles's Law and Boyle's Law?
3. How does temperature conversion from Fahrenheit to Kelvin work?
4. What are some other gas laws used in thermodynamics?
5. Can the ideal gas law be applied here instead of Charles's Law?

Tip: Always remember to use absolute temperatures (Kelvin) in gas law calculations to avoid errors!