Final answer:
Using the combined gas law, if the pressure of an ideal gas is doubled and the temperature is halved, the ratio of the final volume to the initial volume is 1, meaning there is no change in volume.
Step-by-step explanation:
We can solve this problem using the combined gas law, which relates pressure (P), volume (V), and temperature (T) in the following way: PV/T=constant. Initially, let's denote the conditions as P1, V1, and T1, and after the change as P2, V2, and T2.
If the pressure of an ideal gas is doubled, this means that P2 = 2 * P1.
If the temperature is halved, then T2 = 0.5 * T1. Since we know that PV/T is constant, we can set up the equation (P1 * V1) / T1 = (P2 * V2) / T2.
Substituting the doubled pressure and halved temperature into this equation yields (P1 * V1) / T1 = (2 * P1 * V2) / (0.5 * T1).
Solving for the ratio of the final volume to the initial volume, V2/V1, gives us:
V2/V1 = (P1*T1) / (2*P1*0.5*T1) = 1/1, which means that V2 = V1.
Therefore, the ratio of the final volume to the initial volume is 1, indicating that the volume does not change when the pressure is doubled and the absolute temperature is halved.