The volume of a gas is reduced from 4.0 L to 0.5 L while the temperature is held constant. How does the gas pressure change?

Question

BlackTom AI · Accepted Answer

Consider the gas behavior under constant temperature as described by Boyle's law, P ∝ 1/V. This means pressure and volume are inversely related when temperature is fixed.
Option 1: 'It increases by a factor of four.' If the volume drops from 4.0 L to 0.5 L, the volume decreases by a factor of 8, not 4. Under a simple P ∝ 1/V relationship, the pressure would increase by the reciprocal of the volume change, which would be 8, not 4. This makes the stated factor inconsistent with Boyle's law in this scenario.
Option 2: 'It decreases by a factor of eight.' A decrease in pressure would imply either an increase in volume or a violation of the constant-temperature assumption. Since the volume is actually decreasing, pressure should increase, not decrease, so this option contradicts the basic inverse proportionality between P and V when T is constant.
Option 3: 'It increases by a factor of eight.' Here, the volume change is from 4.0 L to 0.5 L, which is a reduction by a factor of 8. With T constant, P must rise by the same factor that V falls by, due to P ∝ 1/V. Therefore, the pressure increases eightfold, aligning with the inverse relationship and the given quantities. This option correctly applies Boyle’s law to the scenario.
Option 4: 'It increases by a factor of two.' A twofold increase would correspond to a volume reduction by a factor of two under constant temperature, which is not the case here. Since V changes by a factor of eight, a factor of two increase would not accurately reflect the inverse P–V relationship described by Boyle's law in this situation.

The volume of a gas is reduced from 4.0 L to 0.5 L while the temperature is held constant. How does the gas pressure change?单项选择题

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