Ok... You picked my interest.
Grill Propane tank. Stored outside over night. Has not been used in several days. Tank has been closed so should be stable. Ambient air temp 54.
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Not sure what this demonstrates. I believe the tank is about 50% full.
When things are stable as in no gas being demanded by a load, there is little driver for the heat transfer thus little measurable cooling effect. Realistically, without any latent heat transfer (boiling of the liquid into gas) you won't see much temperature difference. You need to apply something to cause the "heat to flow"
Try the temperature guage once you have run some hot water along the side of the tank. Where there is liquid the temperature should lower more quickly than where there is gas since the thermal conductivity of the liquid is higher than that of the gas
Heat Transfer Equation: Q=UA delta T Where Q is the transfer of energy (in the form of heat transfer), U is the thermal conductivity, A is the surface area, and delta T is the temperature difference.
Simplified theory - When you pour the hot water on the tank you set the Delta T (in the short term). The A is about the same, so the only difference is the thermal conductivity (U) of the gas and the liquid. Therefore, more heat will be transferred from the warm tank surface to the liquid than the warm tank surface to the gas and the area exposed to the liquid will cool down more quickly. Ain't it wonderful how Thermodynamics works and you thought you'd never use that equation again.