The volume of a gas in cubic centimeters, V, varies inversely with thepressure of the gas in liters per square centimeter, p.When the volume of the gas is 16 cm3, its pressure is 20 L/cm2. Find thevolume of the gas when the pressure is 1.6 L/cm²
Accepted Solution
A:
The volume of the gas when the pressure is [tex]1.6 \mathrm{L} / \mathrm{cm}^{2}[/tex] is 200 [tex]cm^3[/tex]Solution:Given, the volume of a gas in cubic centimeters, V, varies inversely with the pressure of the gas in liters per square centimeter, p. [tex]\text { Then, } V \alpha \frac{1}{p}[/tex][tex]\rightarrow \mathrm{V}=\frac{c}{p}[/tex]where "c" is proportionality constant.Given that when the volume of the gas is 16 [tex]cm^3[/tex] , its pressure is 20 [tex]L/cm^2[/tex]So, substitute the above values in our formula[tex]\begin{array}{l}{\rightarrow 16=\frac{c}{20}} \\\\ {\rightarrow c=16 \times 20 \rightarrow \mathrm{c}=320}\end{array}[/tex]Now let us find the volume of the gas when the pressure is [tex]1.6 \mathrm{L} / \mathrm{cm}^{2}[/tex][tex]\text { Then, } \mathrm{v}=\frac{320}{1.6}=200[/tex]Hence, the volume of the gas is 200 [tex]cm^3[/tex]