Question

What would be the projected temperature of a gas if it starts out at 7L and 312K? Assume the final volume of the gas will be 12L.

Charles law

Answer 1

To solve this using Charles's Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant, we can use the formula:

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

Where:
- \(V_1\) is the initial volume (7L)
- \(T_1\) is the initial temperature (312K)
- \(V_2\) is the final volume (12L)
- \(T_2\) is the final temperature that we want to find

Rearranging the equation to solve for \(T_2\):

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

Now, substituting in the known values:

\[
T_2 = 312 \, \text{K} \times \frac{12 \, \text{L}}{7 \, \text{L}}
\]

Now, calculate \(T_2\):

\[
T_2 = 312 \, \text{K} \times \frac{12}{7} \approx 312 \, \text{K} \times 1.7143 \approx 535.14 \, \text{K}
\]

So, the projected temperature of the gas at a volume of 12L would be approximately **535.14 K**.