Piezothermal effect in a spinning gas

A spinning gas, heated adiabatically through axial compression, is known to exhibit a rotation-dependent heat capacity. However, as equilibrium is approached, an effect is identified here wherein the temperature does not grow homogeneously in the radial direction, but develops a temperature differential with the hottest region on axis, at the maximum of the centrifugal potential energy. This phenomenon, which we call a piezothermal effect, is shown to grow bilinearly with the compression rate and the amplitude of the potential. Numerical simulations confirm a simple model of this effect, which can be generalized to other forms of potential energy and methods of heating.

Figure 1

Piezothermal effect. Step 1: equilibrium at $T_0$. Step 2: instant vertically uniform temperature rise to $T^{*}$ produced by lateral compression. Step 3: pressure balance, under heat insulation, restored through partition displacement $z$.

Figure 2

Temperature profile for fast heating. Black: initial profile; red: upon heating; green: at maximum temperature gradient; blue: at new equilibrium. $(\delta =G=1.0$.)

Figure 3

Density profile for fast heating. Black: initial profile; red: upon heating; green: at maximum temperature gradient; blue: at new equilibrium. ($\delta =G=1.0$.) Density is normalized to homogeneous one, i.e., total number of particles over total volume.

Figure 4

Spinning gas normalized density profile. Black: initial profile; red: upon heating; green: at maximum temperature gradient; blue: new equilibrium. (Fast heating; $\delta =8/3$; ${\phi }_0=2.74$.)

Figure 5

Spinning gas temperature profile. Black: initial profile; red: upon heating; green: at maximum temperature gradient; blue: new equilibrium. (Fast heating; $\delta =8/3$; ${\phi }_0=2.74$.)