To solve this problem, we can again use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is constant. The formula remains the same: P1V1 = P2V2.
Given: P1 = 1.5 ATM (initial pressure) V1 = Initial volume V2 = 1/4 V1 (final volume)
To find the final pressure, P2, we need to determine the final volume, V2. Let's calculate it:
V2 = 1/4 V1
Now, we can substitute the values into the formula and solve for P2:
P1V1 = P2V2
(1.5 ATM)(V1) = P2(1/4 V1)
Dividing both sides of the equation by V1:
1.5 ATM = P2(1/4)
To isolate P2, we multiply both sides of the equation by 4:
(1.5 ATM)(4) = P2
6 ATM = P2
Therefore, the new pressure of the gas after being compressed isothermally to 1/4 of its original volume is 6 atmospheres.