To find the ratio of P2 to P3, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
According to Boyle's Law:
P1 * V1 = P2 * V2 = P3 * V3
Given: V1 = 15 cm³ V2 = 10 cm³ V3 = 5 cm³
Let's solve for the ratio P2/P3:
P1 * V1 = P2 * V2
P2 = (P1 * V1) / V2
P3 * V3 = P2 * V2
P3 = (P2 * V2) / V3
Substituting the values:
P2 = (P1 * 15 cm³) / 10 cm³ P3 = (P2 * 10 cm³) / 5 cm³
Canceling out the common units:
P2 = (P1 * 15) / 10 P3 = (P2 * 10) / 5
Simplifying further:
P2 = (3/2) * P1 P3 = (2/3) * P2
Substituting the value of P2 into P3:
P3 = (2/3) * [(3/2) * P1]
Simplifying the expression:
P3 = (1) * P1
Therefore, the ratio of P2/P3 is:
P2/P3 = [(3/2) * P1] / P1 P2/P3 = 3/2
So, the ratio of P2 to P3 is 3/2 or 1.5.