Question

What would be the projected volume of gas if it starts out at 5L and 450K? Assume the final temperature of the gas will be 381K
Charles law

Answer 1

Charles's law states that the volume of a gas is directly proportional to its absolute temperature when the pressure is held constant. The law can be expressed with the formula:

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

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.

Given:
- \( V_1 = 5 \, \text{L} \)
- \( T_1 = 450 \, \text{K} \)
- \( T_2 = 381 \, \text{K} \)

We want to find \( V_2 \). Rearranging the equation gives:

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

Now substituting the known values:

\[
V_2 = 5 \, \text{L} \cdot \frac{381 \, \text{K}}{450 \, \text{K}}
\]

Calculating \( V_2 \):

\[
V_2 = 5 \, \text{L} \cdot \frac{381}{450} \approx 5 \, \text{L} \cdot 0.8467 \approx 4.2335 \, \text{L}
\]

Therefore, the projected volume of the gas at a temperature of 381 K would be approximately **4.23 L**.