Step 1 - Understanding the relation between temperature and volume for a gas
There are three important variables that can modify the state of a gas: pressure, temperature and volume. They're all related by the ideal gas equation.
When pressure is kept constant, we can simplify this relation: temperature and volume become proportional, i.e., the greater the temperature, the greater the volume. This can be stated mathematically as:
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]
Step 2 - Substituting the values to solve the problem
From the exercise, we know that:
[tex]\begin{gathered} V_1=50\text{ L} \\ \\ T_1=25\degree C\text{ (298 K)} \\ \\ T_2=45\degree C(318\text{ K)} \\ \\ V_2=\text{ ?} \end{gathered}[/tex]
Note that we have converted all temperatures to Kelvin. That's because the proportionality between volume and temperature only work in K, the absolute temperature.
Substituting the values on the equation:
[tex]\frac{50}{298}=\frac{V_2}{318}\rightarrow V_2=\frac{318\times50}{298}=53.33\text{ L}[/tex]
The final volume will be thus 53.33 L.
