the volume V of a gas at a constant temperature varies inversely with the pressure P. when the volume is 100 cubic inches the pressure is 25 pounds per square inch. what is the pressure when the volume is 125 cubic inches
Accepted Solution
A:
Answer:The pressure is [tex]20\ psi[/tex]Step-by-step explanation:we know thatA relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]In this problem we have [tex]V*P=k[/tex]whereV is the volume of a gas at a constant temperatureP is the pressurewe haveFor [tex]V=100\ in^{3}[/tex],[tex]P=25\ psi[/tex]step 1Find the value of ksubstitute the values of V and P [tex]100*25=k[/tex] [tex]k=2,500[/tex]The equation is equal to [tex]V*P=2,500[/tex]step 2Find the pressure when the volume is 125 cubic inchesFor [tex]V=125\ in^{3}[/tex]substitute in the equation and solve for P[tex]125*P=2,500[/tex][tex]P=2,500/125=20\ psi[/tex]