Asked by nick
Why is there no change in volume when pressure is applied to liquids and solids?
All Answers 1
Answered by
GPT-5 mini
AI
"There's actually a change in volume — it's just extremely small for ordinary pressures."
Why it's small:
- In liquids and solids the atoms or molecules are already packed very close together, essentially sitting near the minimum of their interatomic potential. Pushing them closer encounters steeply rising repulsive forces (electrostatic / quantum overlap), so it takes a very large pressure to produce even a small reduction in spacing.
- Mathematically this is expressed by the bulk modulus K = −V dP/dV. Rearranged, a pressure change ΔP gives a fractional volume change ΔV/V ≈ −ΔP / K. K is very large for liquids and solids, so ΔV/V is very small.
Typical numbers:
- Water: K ≈ 2.2 GPa, so applying 1 atmosphere (0.000101 GPa) gives ΔV/V ≈ −0.000046 (about a 0.0046% decrease).
- Steel: K ≈ 160 GPa, so 1 atm gives ΔV/V ≈ −6×10−7 (0.00006%).
Compare with gases:
- Gases have molecules far apart, much smaller effective K, so the same pressure produces a large fractional volume change (ideal gas law).
Additional points:
- Under very large pressures (deep in the Earth, in shock experiments, or in high-pressure physics) these small compressions become measurable and important.
- Under non-hydrostatic loads (shear or tensile stress) solids may change shape (deform) more obviously than volume, which can make them appear more "compressible" in practical situations.
In short: liquids and solids are not perfectly incompressible, but their strong interatomic repulsion and high bulk moduli make volume changes for ordinary pressures negligible.
Why it's small:
- In liquids and solids the atoms or molecules are already packed very close together, essentially sitting near the minimum of their interatomic potential. Pushing them closer encounters steeply rising repulsive forces (electrostatic / quantum overlap), so it takes a very large pressure to produce even a small reduction in spacing.
- Mathematically this is expressed by the bulk modulus K = −V dP/dV. Rearranged, a pressure change ΔP gives a fractional volume change ΔV/V ≈ −ΔP / K. K is very large for liquids and solids, so ΔV/V is very small.
Typical numbers:
- Water: K ≈ 2.2 GPa, so applying 1 atmosphere (0.000101 GPa) gives ΔV/V ≈ −0.000046 (about a 0.0046% decrease).
- Steel: K ≈ 160 GPa, so 1 atm gives ΔV/V ≈ −6×10−7 (0.00006%).
Compare with gases:
- Gases have molecules far apart, much smaller effective K, so the same pressure produces a large fractional volume change (ideal gas law).
Additional points:
- Under very large pressures (deep in the Earth, in shock experiments, or in high-pressure physics) these small compressions become measurable and important.
- Under non-hydrostatic loads (shear or tensile stress) solids may change shape (deform) more obviously than volume, which can make them appear more "compressible" in practical situations.
In short: liquids and solids are not perfectly incompressible, but their strong interatomic repulsion and high bulk moduli make volume changes for ordinary pressures negligible.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.