According to Charle's law, the volume of the given mass of a gas is directly proportional to its absolute temperature provided that the pressure is constant. Mathemically;
[tex]\begin{gathered} V\alpha T \\ V=kT \\ k=\frac{V}{T} \\ k=\frac{V_1}{T_1}=\frac{V_2}{T_2} \end{gathered}[/tex]where;
V1 and V2 are the initial and final volume of the gas
T1 and T2 are the initial and final temperatures of the gas (in Kelvin)
Given the following parameters:
[tex]\begin{gathered} V_1=100\operatorname{cm}^3 \\ T_1=27^0C=27+273=300K \\ T_2=20^0C=20+273=293K \\ V_2=\text{?} \end{gathered}[/tex]Substitute the given parameters into the formula;
[tex]\begin{gathered} V_2=\frac{V_1T_2}{T_1}^{} \\ V_2=\frac{100\times293}{300} \\ V_2=\frac{29300}{300} \\ V_2=\frac{293}{3} \\ V_2=97.67\operatorname{cm}^3 \end{gathered}[/tex]Therefore the volume of the gas at 20°C is approximately 97.67cm³
