Theory

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Conduction

Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree in a specified way. This can be further defined depending on if the volume or pressure are kept constant. For example, specific heat at constant pressure is the energy required to raise the temperature of a unit mass of a substance by one degree as the pressure is maintained constant.

The specific heat of a substance changes with temperature:

cp = Specific Heat at Constant Pressure

h = Enthalpy

T = Temperature

This shows that cp is the partial derivative of enthalpy over time with respect to pressure.

In a lava lamp the two substances have a similar cp value so that a similar amount of energy can be transferred to each using the same heating element, usually a light bulb. This is important as it ensures the flow of convection currents in the lava lamp are maintained.

In an ideal situation, the lava lamp system would be adiabatic, meaning that no heat is transferred between it and the surrounding air. This will not entirely be the case as heat will always be transferred to the surrounding assuming that the surroundings are cooler then the lamp itself. The theoretical amount of energy per unit mass needed to heat the liquid can be calculated using the following:

q = Heat per unit Mass cp = Specific Heat at Constant Pressure

ΔT = Change in Temperature

Forming Bubbles

Two substances are used in lavas lamps, usually paraffin wax and water-alcohol mix. These do not mix as the wax is hydrophobic. This allows the substances to remain separate with their different intensive properties; these are properties that are independent of mass, such as density.

ρ = Density m = Mass

V = Volume

Specific gravity is the ratio of the density of a substance to the density of some standard substance at a specified temperature (usually water at 4°C).

SG = Specific Gravity

ρ = Density of Substance

ρH2O = Density of Water

In the case of the lava lamp:

SG = Specific Gravity ρwax = Density of Wax

ρwater = Density of Water

Density decreases as temperature increases due to the volume increase as the particles gain more energy causing them to move with higher velocities. Once SG is less than 1 the wax will begin to float upwards as its density is now less than the density of the water.

Convection Currents

Convection currents is the movement of molecules in a fluid caused by heat transfer. Heat always moves from an area of high heat to an area of low heat. Temperature effects the density of a substance, therefore a change in temperature will cause a change in density and therefore a change in density ratios with surrounding molecules. This is what causes the molecules to move.

Lava lamps act as a closed system where no mass can cross in or out of the boundary, but energy can. The light bulb at the bottom of the lava lamp heats up the liquid making it less dense and causing it to rise. Due to the shape of the lava lamp container, the top is cooler than the bottom. This means that the rising bubbles will lose their heat to their surroundings, including the cooler liquid. This loss of heat causes them to become denser again so that they sink back down to the bottom of the lava lamp and the cycle begins again. This happens with both the water and the wax but is more noticeable with the wax.