# A hot air balloon is filled with 1.89 x 10^2 liters of air at 21 C. If atmospheric pressure does not change, how hot must the air become in order to increase the volume to 4.5 x 10^2 liters?

We use $\text{Charles' Law}$ ${V}_{2} / {T}_{2} = {V}_{1} / {T}_{1}$. ${T}_{2}$ will at least double ${T}_{1}$.
$\text{Charles' Law}$ states that a given quantity of gas has a volume directly proportional to the absolute temperature:
$V \propto T$, else $V = k T$. Solving for $k$, ${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$, and ${T}_{2} = {V}_{2} / {V}_{1} \times {T}_{1}$
${T}_{2} = \frac{4.5 \times {10}^{2} \cdot L}{1.89 \times {10}^{2} \cdot L} \times 294 \cdot K$ $=$ ??K