When the temperature and number of particles of a gas are constant, which of the following is also constant?

Question

BlackTom AI · Accepted Answer

To analyze this question, I’ll consider what remains constant when temperature and number of particles are fixed for a gas.
Option 1: the sum of the pressure and volume. If T and n are constant, Boyle's law tells us P is inversely proportional to V (P ∝ 1/V). The sum P + V would vary as V changes, so this sum is not generally constant. Misconception here is treating P and V as independent even though they trade off with each other under constant T and n.
Option 2: the difference of the pressure and volume. Similar to the sum, P − V would also change as V changes to satisfy the gas law. There isn’t a reason for their difference to stay fixed when P and V adjust to maintain P ∝ 1/V. This choice ignores the inverse relationship between P and V.
Option 3: the product of the pressure and volume. Under constant temperature and amount of gas, Boyle’s law states that P × V = constant. This is the defining relationship that preserves a fixed product when T and n do not change. The key concept here is that pressure and volume compress or expand in a way that keeps their product the same.
Option 4: the ratio of the pressure and volume. While P/V does change with V unless P changes in just the right way, there is no general principle guaranteeing P/V is constant for a fixed T and n. The ratio depends on the particular state and does not stay fixed in all scenarios described by the problem.
In summary, the only option that aligns with the standard gas law under constant T and n is the product P × V, which remains constant as P and V vary inversely to one another. The other options fail because they rely on additive or ratio relationships that do not hold constant in Boyle’s framework.

When the temperature and number of particles of a gas are constant, which of the following is also constant?Single choice

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