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Answer, and give a reason. Why can a gas have a bulk modulus but no Young's modulus or shear…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Answer, and give a reason.
- Why can a gas have a bulk modulus but no Young's modulus or shear modulus?
- A liquid is called incompressible. Is its bulk modulus small or large?
- Under a hydraulic stress, which changes: the shape or the volume?
Need a reminder? The key ideaShow
Bulk modulus: ; compressibility . Water: . A gas at a steady temperature has . For a cube, each edge shrinks by a third of the fractional change of volume.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. (a) A gas has no shape of its own, so it cannot be stretched or sheared into a new shape and push back. It does push back when squeezed, so it has a bulk modulus.
Step 2. (b) Large: a big pressure gives only a tiny change of volume.
Step 3. (c) The volume. An equal pressure on every side keeps the shape.
Answer: (a) No shape to keep. (b) Large. (c) The volume.
Watch out. 'Incompressible' is an approximation; water's volume does shrink, by about for each atmospheres.
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