To solve the problem, we can use Charle's law, which states that for an ideal gas at constant pressure the ratio between absolute temperature T and volume V remains constant:
[tex] \frac{T}{V}=k [/tex]
For a gas transformation, this law can be rewritten as
[tex] \frac{T_1}{V_1}= \frac{T_2}{V_2} [/tex] (1)
where 1 and 2 label the initial and final conditions of the gas.
Before applying the law, we must convert the temperatures in Kelvin:
[tex]T_1 = 50^{\circ}C + 273 = 323 K[/tex]
[tex]T_2 = 100^{\circ}C+273=373 K[/tex]
The initial volume of the gas is [tex]V_1 = 5 L[/tex], so if we re-arrange (1) we find the new volume of the gas:
[tex]V_2 = V_1 \frac{T_2}{T_1}=(5 L) \frac{373 K}{323 K}=5.77 L [/tex]
