Answer: The volume of an ideal gas will triple in value if the pressure is reduced to one-third of its initial value
Explanation:
We can determine this from the gas laws. Using Boyle's law, which states that "the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature"
Mathematically, P ∝ (1/V)
Since P ∝ (1/V), we can then write that
P = k(1/V)
Where P is the pressure, V is the volume and k is the proportionality constant
PV = k
We can then write that
P1V1 = P2V2 = P3V3 = ...
Hence, P1V1 = P2V2
Where P1 is the initial pressure of the gas
P2 is the final pressure of the gas
V1 is the initial volume of the gas
and V2 is the final volume of the gas
From the question, we want to determine what will make the new volume be thrice the initial volume.
Hence,
P1 = P
V1 = V
P2= ??
V2 = 3V
Therefore,
P × V = P2 × (3V)
P2 = PV/3V
P2 = P/3 = 1/3(P)
This means the volume of an ideal gas will triple in value if the pressure is reduced to one-third of its initial value
D. All of the above
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