Answer : The final volume of a gas is, [tex]316.96cm^3[/tex]
Explanation :
According to the Charles's law, the volume of a gas is directly proportional to the temperature of the gas at constant pressure and the number of moles of gas.
[tex]V\propto T[/tex]
or,
[tex]\frac{V_1}{V_2}=\frac{T_1}{T_2}[/tex]
where,
[tex]V_1[/tex] = initial volume of gas = [tex]524cm^3[/tex]
[tex]V_2[/tex] = final volume of gas = ?
[tex]T_1[/tex] = initial temperature of gas = 491 K
[tex]T_2[/tex] = final temperature of gas = 297 K
Now put all the given values in the above formula, we get the final volume of a gas.
[tex]\frac{524cm^3}{V_2}=\frac{491K}{297K}[/tex]
[tex]V_2=316.96cm^3[/tex]
Therefore, the final volume of a gas is, [tex]316.96cm^3[/tex]
