More Ethanol

More extensive data for ethanol \(CH_3CH_2OH\) is presented below,

Temp (K)	Densityx10^3 (kg/m3)	v boom (m/s)	T boom (K)	n
378.15	706	93.284	16.07	23.53
373.15	711	93.945	16.30	22.89
368.15	717	94.738	16.58	22.21
363.15	722	95.398	16.81	21.60
358.15	728	96.191	17.09	20.96
353.15	733	96.852	17.32	20.38
348.15	738	97.513	17.56	19.82
343.15	743	98.173	17.80	19.28
338.15	748	98.834	18.04	18.74
333.15	753	99.494	18.28	18.22
328.15	758	100.155	18.53	17.71
323.15	763	100.816	18.77	17.21
318.15	768	101.476	19.02	16.73
313.15	772	102.005	19.22	16.30
308.15	777	102.666	19.47	15.83
303.15	781	103.194	19.67	15.41
298.15	786	103.855	19.92	14.97
293.15	790	104.383	20.12	14.57
288.15	795	105.044	20.38	14.14
283.15	799	105.572	20.59	13.76
278.15	803	106.101	20.79	13.38
273.15	808	106.762	21.05	12.98
268.15	812	107.290	21.26	12.61
263.15	816	107.819	21.47	12.26
258.15	820	108.347	21.68	11.91
253.15	824	108.876	21.89	11.56
248.15	828	109.404	22.11	11.23
243.15	832	109.933	22.32	10.89
238.15	836	110.461	22.54	10.57
233.15	840	110.990	22.75	10.25
228.15	844	111.518	22.97	9.93
223.15	848	112.047	23.19	9.62
218.15	851	112.443	23.35	9.34
213.15	855	112.972	23.57	9.04
208.15	859	113.500	23.79	8.75
203.15	863	114.029	24.01	8.46
198.15	866	114.425	24.18	8.19
193.15	870	114.954	24.41	7.91
188.15	874	115.482	24.63	7.64
183.15	877	115.879	24.80	7.38
178.15	881	116.407	25.03	7.12
173.15	884	116.804	25.20	6.87
168.15	888	117.332	25.43	6.61
163.15	891	117.729	25.60	6.37

\(n\) increases as temperature increases throughout the range of temperature presented, and beyond the boiling point at \(351.39\,K\).

\(n\) increasing with temperature is consistent with increasing thermal energy \(\cfrac{3}{2}kT\) with temperature, but clustered particles seem intuitively less likely to increase in size with temperature.  Increase in collisions is likely to break clustered particles apart.  BUT density is decreasing, that means there is more space between particles as temperature increases.  Maybe collisions decreases with lowered density and clustering increases with temperature as density drops, with more space between clustered particles.

Taken to higher temperature, before disintegration, clustering could result in large macro-molecules in high velocity.  Is that possible?  The least value of \(n\) is one, \(n\ge1\)

What is the nature of such clustering?  Temperature particles acting like waves and coalesce?  Is clustering electrostatic as the particles break from the lattice are positively charged.

Is \(n\) even valid?