Gas laws — Boyle (PV const at T), Charles (V - T const at P), Gay-Lussac (P - T const at V): Question bank

Before you start, re-anchor the three "frozen knob" ideas: Boyle freezes ==temperature $T$ , Charles freezes pressure $P$ , Gay-Lussac freezes volume $V$ == — all three also freeze the amount $n$ (moles). Everything below tests whether you truly know which knob is frozen and why.

True or false — justify

Boyle's law needs temperature to be constant, not just unchanged at the endpoints.

True —

P V

stays constant only if

T

is held fixed throughout; if

T

dips and returns,

P V

can wander in between, so the whole path must be isothermal.

Doubling the Celsius temperature at constant pressure doubles the volume.

False — Charles is proportional to absolute (Kelvin) temperature;

2 0^{\circ} C \to 4 0^{\circ} C

293 K \to 313 K

, only a

\sim 7%

rise in

V

, nowhere near double.

0^{\circ} C

the molecules of an ideal gas have stopped moving.

False —

0^{\circ} C = 273.15 K

, so molecules still have plenty of kinetic energy; motion only ceases (idealised) at

0 K

, i.e.

- 273.1 5^{\circ} C

For a fixed mass of ideal gas,

P V / T

is the same number no matter how you change

P

V

, or

T

True —

P V / T = n R

, and for fixed

n

(with

R

the universal gas constant) this is a constant, which is exactly why the combined law

P_{1} V_{1} / T_{1} = P_{2} V_{2} / T_{2}

works.

P

-vs-

1/ V

plot for Boyle's law is a straight line through the origin.

True — since

P = (n R T) \cdot (1/ V)

, plotting

P

against

1/ V

gives a line with slope

n R T

passing through the origin at constant

T

and

n

(middle panel of the figure above).

If you double the number of moles at constant

P

and

T

, the volume is unchanged.

False —

V = (n R T / P)

, so doubling

n

doubles

V

; none of Boyle/Charles/Gay-Lussac apply here because they all assume

n

is fixed (this is Avogadro's territory).

Gay-Lussac's law explains why a sealed aerosol can bursts in a fire.

True — rigid can means constant

V

, so heating raises

T

and thus

P

(since

P \propto T

), until the wall can no longer hold the pressure.

The graph of

P V

against

P

for an ideal gas at fixed

T

is a horizontal line.

True —

P V = n R T

is constant when

T

and

n

are fixed, so it does not vary with

P

; a real gas would deviate, curving away from horizontal.

Charles's law lets you predict a positive volume at

- 30 0^{\circ} C

False —

- 30 0^{\circ} C

is below absolute zero (

- 273.1 5^{\circ} C

), which the ideal-gas extrapolation forbids; the law's linear extrapolation reaches

V = 0

0 K

and cannot continue past it (right panel of the figure above).

Spot the error

"A gas goes from

2 L

300 K

4 L

; by Boyle's law the pressure halves."

Error — Boyle requires constant

T

, but the final temperature is never given, so you cannot assume it stayed at

300 K

. Without that missing final

T

(or, equivalently, a stated final pressure) even the combined law

P_{1} V_{1} / T_{1} = P_{2} V_{2} / T_{2}

has too many unknowns to solve; the "pressure halves" claim silently assumes constant

T

, which nothing in the problem justifies.

"Heating a gas from

2 5^{\circ} C

5 0^{\circ} C

at constant

P

doubles its volume because

50/25 = 2

Error — you must convert to Kelvin:

298 K \to 323 K

, a ratio of about

1.08

, so the volume rises only

\sim 8%

, not

100%

"In Gay-Lussac's law,

P_{1} / T_{1} = P_{2} / T_{2}

works with

T

in Celsius as long as both sides use the same unit."

Error — the law is a proportionality to absolute

T

; using Celsius can give division by zero or negative temperatures, and equal-looking ratios in

^{\circ} C

are not the true physical ratios.

"A balloon's volume should follow Gay-Lussac's law when you warm it."

Error — a balloon sits at (roughly) constant atmospheric pressure with a flexible skin, so it obeys Charles (constant

P

); Gay-Lussac needs a rigid, constant-volume container.

"Since Boyle's law has no

T

term, temperature is irrelevant to it."

Error —

T

isn't in the two-state form only because it cancels after being held constant; if

T

were allowed to change,

P V

would change too, so a constant

T

is a hidden requirement.

P V = n R T

, so if I compress a gas isothermally, its temperature rises because I did work on it."

Error — isothermal means

T

is held constant by design (heat flows out to the surroundings); the equation still holds with the same

T

, and

P V

stays constant.

Why questions

Why must Charles's and Gay-Lussac's laws use Kelvin but Boyle's law needs no temperature conversion?

Charles/Gay-Lussac are direct proportionalities to absolute

T

, so the zero of the scale matters and only Kelvin has its zero at true "no thermal energy"; in Boyle's law

T

is merely held fixed and cancels, so its scale never enters.

Why does halving a gas's volume double its pressure microscopically?

Packing the same molecules into half the space doubles their number density, so they strike each unit of wall twice as often, and (at fixed

T

, so fixed speeds) doubling the hit rate doubles the pressure.

Why does the

V

-vs-temperature line for every ideal gas extrapolate to the same point?

All ideal gases follow

V = (n R / P) T

with the same universal

R

, a line whose extrapolation reaches

V = 0

exactly when

T = 0 K

regardless of the gas identity, which is precisely how absolute zero is defined.

Why can we treat

n R T

as "the constant" in Boyle's law?

Because Boyle freezes both

T

and

n

, and

R

is a universal constant, so the entire product

n R T

is a single fixed number that

P V

must equal.

Why does heating a gas at constant pressure require its volume to grow?

Hotter molecules move faster and would hit the walls harder and more often; to keep pressure fixed, the gas must spread into a larger volume so the hit frequency per unit area falls back down.

Why does the combined gas law reduce to each single law?

P_{1} V_{1} / T_{1} = P_{2} V_{2} / T_{2}

, setting one variable equal on both sides makes it cancel, leaving

P_{1} V_{1} = P_{2} V_{2}

(Boyle),

V_{1} / T_{1} = V_{2} / T_{2}

(Charles), or

P_{1} / T_{1} = P_{2} / T_{2}

(Gay-Lussac).

Edge cases

What happens to Boyle's-law pressure as volume approaches zero?

P = n R T / V

diverges to infinity as

V \to 0

; physically a real gas resists this long before, because molecules have finite size and the ideal model breaks down under extreme compression.

If temperature is held at exactly

0 K

in Charles's law, what volume is predicted?

V = (n R / P) \cdot 0 = 0

; the ideal gas would occupy zero volume, which is the unreachable limit marking absolute zero, not a real achievable state.

Does Boyle's law hold for a real gas at very high pressure?

No — at high pressure intermolecular forces and finite molecular volume matter, so

P V

drifts from constant; Boyle is a low-pressure, ideal-gas approximation.

What does the combined gas law say if all three of

P

V

T

change at once?

It still holds:

P_{1} V_{1} / T_{1} = P_{2} V_{2} / T_{2}

links the initial and final states regardless of the path, as long as

n

is fixed — no single-law shortcut applies.

n

changes during a process, can any of Boyle/Charles/Gay-Lussac be used?

No — all three (and the combined law in the boxed form) assume fixed

n

; a changing amount needs the full

P V = n R T

or Avogadro's law to account for the new moles.

What is the pressure of an ideal gas at absolute zero and constant volume, by Gay-Lussac?

P = (n R / V) \cdot 0 = 0

; the extrapolated pressure vanishes at

0 K

, the same limiting behaviour that defines absolute zero from the pressure side.

Connections

Ideal Gas Equation PV=nRT — every trap here traces back to freezing one variable in this equation.
Absolute Zero and Kelvin Scale — the source of all the Kelvin-vs-Celsius traps.
Combined Gas Law — the unifier that resolves "which law applies" confusion.
Kinetic Theory of Gases — the microscopic "why" behind the pressure answers.
Avogadro's Law — governs the fixed- $n$ edge cases above.