What Is a Fluid? — Question 4

Question 4

An opened partition distinguishes two fluids

A rigid vessel has two equal $1.0\,\mathrm{L}$ compartments separated by a removable partition. A sample initially fills the left compartment; the right is evacuated. Consider two separate experiments: an idealized nonvolatile liquid with negligible compressibility, and a gas. Remove the partition and wait for equilibrium at the original temperature. For the liquid, gravity acts downward and the compartments have equal horizontal base areas; ignore capillarity.

1. Compare the final volume occupied by each sample. If the initial liquid depth is $h$, what is its final depth?

2. Both samples adapt to container shape. Why does that fact alone fail to distinguish a liquid from a gas, or to define all fluids?

Question 4 - Solution

An opened partition distinguishes two fluids

(a) Derivation and calculation

Let each compartment have base area $A_b$. Incompressibility gives$$V_{\ell,f}=V_{\ell,i}=A_bh=1.0\,\mathrm L.$$$$2A_bh_f=A_bh\Rightarrow\boxed{h_f=h/2}.$$$$\boxed{V_{g,f}=2.0\,\mathrm L},\qquad\boxed{V_{\ell,f}=1.0\,\mathrm L}.$$

(b) Result and interpretation

With unchanged mass,$$\rho_{\ell,f}\simeq\rho_{\ell,i},\qquad\rho_{g,f}=\frac{m}{2V_{g,i}}=\frac12\rho_{g,i}.$$Shape adaptation occurs in both fluids and can also occur in a deformed solid. Sustained-shear response distinguishes ordinary fluids from solids; volume response distinguishes the specified liquid and gas.

Physical check

The liquid occupies half the total vessel volume, leaving space above its free surface.