pipette waterfountain Place the tip of a pipette in some hot water.  Cover the other end with you thumb.  Invert the pipette and water sprays out nearly two metres.  
Is the cool air in the pipette being heated by the hot water and thus expanding to force some of the water to spray out?  Does the ideal gas law apply?  Is this as fun for other people as it is for me?
 A: Theoretical Background
The pipette's ability to hold water with a seal covering the top, occurs due to the balance of forces. One of these forces is surface tension, a combination of the cohesive forces holding together the liquid molecules and the adhesive electrostatic attraction between the liquid and pipette wall (Perlman, 2016). This force coupled with upwards air pressure is equal to a force of gravity, resulting in the water remaining stationary. 
As heat is directly proportional to internal energy, when the experiment is performed with hot water the molecules have more kinetic energy and weaker intermolecular bonds between molecules. This results in a decrease in both adhesive and cohesive forces, therefore lowering the surface tension (Nave, 2016).
The hot water fountain phenomenon occurs when a pipette with hot water trapped in the lower half is flipped. This movement momentarily disturbs the surface tension, allowing a small amount of water to run down the side of the pipette. The subsequent gas expansion is explained by Fourier’s Law (Mechanical Engineering, 2016):
dQ/dt=h .A .∆T
dQ/dt=heat transfer
h=heat transfer coefficient 
∆T=temperature change
A=surface area 
dQ/dt∝A 
∴heat transfer∝surface area
As the water runs down the side, there is an increased surface area of water molecules working to transfer heat to air particles. Hence the increase in heat transfer causes an increased rate of gas expansion, further explaining its sudden acceleration. 
Additionally, Fourier’s Law also highlights: 
dQ/dt∝∆T
∴heat transfer∝temperature change
This showcases that an increased temperature differential between the liquid and the air particles in the pipette would significantly increase the height of the fountain. Additionally, the gas expansion pushing a smaller volume of water with a lower weight would be certainly propelled by the gas expansion, while larger column of water with a greater weight would be effected less by the same gas expansion.
Furthermore, an increase of the liquid temperature results in weakened cohesive and adhesive forces, therefore showing that water at a higher temperature would be affected to a larger extent by the momentary disturbance in the surface tension, caused by the flipping motion. As explained above, this allows more water to slide down the sides of the pipette, hence increasing gas expansion and projection height. This effect can be emphasized by adding detergent to water to further lower its surface tension. 
This expansion of gas pushes the water through the tapered end, which further increases its velocity, as per Boyle's Law and The Continuity Principle. Firstly, Boyle's Law explains the inverse relationship between pressure and volume, in which a decreased volume results in particles hitting the sides of the container more often, thus increasing the pressure (Hall, 2015). This increase in pressure results in more force pushing the water molecules, and hence an increased velocity. 
P ∝  1/V
P=Pressure
V=Volume
Further, the Continuity Principle states that the mass flow rate must be equal inside the pipette, compared to the water that leaves the tapered tip. As the density of water remains unchanged, this principle can be simplified to show the discharge is equal, and thus (Bryant, 2015): 
∴Q_1= Q_2
∴A_1 u_1= A_2 u_2
A=cross sectional area of pipette
u=velocity
u_2=  A_1/A_2  u_1=  (π .  r_1^2  )/(π  .  r_2^2  ) u_1=  (r_1^2)/(r_2^2 ) u_1
∴u_2= (r_1/r_2 )^2 u_1
∴Exit velocity dependent on ratio of diameters (inside of pipette vs tapered end)
∴u_2= (r_1/r_2 )^2 u_1
Substituting the known values of the radius, we can obtain an expression relating the velocity of the liquid before and after its interaction with the tapered end.
u_2=(0.0025/0.0005)^2 u_1
u_2=25 ×u_1
The tapered pipette further accelerates the water, adding to the expanding gas's transferred energy and velocity.  
