How does the temperature affect the viscosity of glycerol?

In addition to comparing the curve of best fit, I have decided to linearise all discrete values to obtain linear graphs to conduct further analysis. We know that our model is η=AT^B therefore we can use logarithmic both sides:

ln η = ln AT ^B
⇒ ln η = B ln T + ln A

which is comparable to our linear equation

y = mx + b

where y =  ln η,x = ln T, b =  ln A and m = B, therefore we must plot ln η against lnT. To calculate the uncertainties, I will consider all min and max values from uncertainties for each individual discrete temperature and viscosity and linearise them. I will then find the uncertainty by considering the difference between min and max values and dividing it by 2:

• Micrometer of uncertainty \(±5\ \times\ 10^{-6}m\)
• Digital sale of uncertainty \(±5\ \times\ 10^{-6}kg\)
• \(\times\ 2\) long measuring cylinders of 250ml of uncertainty ± 1m;
• \(\times\ 2\) beakers
• Meter ruler of uncertainty \(±5\ \times\ 10^{-4}m\)
• Thermometer of uncertainty \(±0.05^oC\)
• iPhone Camera
• Glycerol
• Styrofoam
• A sphere more dense than glycerol

1. The method at which the ball is dropped- in order to ensure that the ball does not gain any extra acceleration from the throw of my hand, the ball has to be ”dropped” by letting gravity accelerate the ball from the same place.
2. The mass and the size of the ball- The volume of the mass of the ball cannot change as it would directly affect the velocity observed. Thus, this has to be kept constant.
3. The volume of Glycerol- The volume of the glycerol would also affect the velocity of the ball in the fluid as a result of pressure; hence this must also be kept constant at250ml
4. Distance between measuring cylinder and camera- In order to ensure that any possible parallax errors are systematic rather than random between each experiment, if any, the distance between camera for observation and cylinder is kept the same.

However, graphing our results is trickier than my initial thought. There is no comparable theoretical basis for the estimation of liquid viscosities. Thus, it is particularly desirable to determine liquid viscosities from experimental data when such data exists (Robert C. Reid, 1987, p.517). Many models exist to explain the behavior of viscosity against temperature, and however, for the purpose of this Internal Assessment, I will consider a widely used empirical equation using my own and literature discrete values. I then will compare these constants found between my values, discrete literature values, and literature values of constants found by the same scientist who used this equation. The discrete literature values I will use for the analysis of separate equations are the following (Association, 1963)

I believe that lower temperatures of glycerol will result in higher viscosity, and higher temperatures will result in lower viscosity. As the temperature is defined to be the average kinetic energy of a particle in a material, the lower the temperature, the lower the average kinetic energy in a particle. As a result, less space is occupied by particles as they come closer together, implying higher density. Consequently, a larger number for the density of glycerol ρ_g (from lower temperature) means that ρ_b−ρ_g  is a smaller number. Knowing that velocity is a constant if we achieve a smaller number for ρ_b−ρ_g in the numerator, the viscosityηmust be a smaller value due to its direct proportionality. Whilst the direct proportionality between the density difference and viscosity suggests the idea that the viscosity decreases, I believe there will be a substantial change in viscosity independent of the density, which will outweigh the density change as the temperature varies. When I introduce the variable T temperature into the equation, I believe the density change will be minimal. If we consider equation 3 during terminal velocity:

\(0=F_D-{\rm kv}_e\)​​​​​​​

Since my velocity is a constant and I hypothesize that the density difference is minimal, we can assume that F_D is also a constant. This means that my temperature must affect k. However,k = 6πηr and r and 6π are constants. Therefore, the temperature will directly affect η. The relationship betweenTandη, however, is described to be” no comprehensive theory on the viscosity of liquids so far because of its complex nature.” (Association, 1963). Therefore there also does not exist an equation that perfectly describes the relationship ofηandT. However, I do believe that as the temperature increases, the viscosity will decrease, which will also result in the decrease of the drag force. This means less energy is required to break the bonds between the ball and glycerol. This energy is provided by gravitational energy mgh, and since less energy is provided into the system to break these bonds, it is naturally transferred into kinetic energy, implying an increase in the constant velocity. Therefore, with this hypothesis, I must also observe an increase in my value of constant velocity.

1. The beaker’s height is measured using a meter ruler. This value is then halved and then marked in the beaker with a red marker. Furthermore, the beaker is also covered is surrounded with heat-insulating material in order to minimize energy transfer between surroundings and glycerol. The beaker is then placed on top of the digital scale.
2. A thermometer is placed inside a bowl filled with glycerol which is placed in a bath of water. This bath is then heated until the desired temperature. If the glycerol is overheated, it is then left at room temperature until it reaches desired temperatures.
3. The glycerol that requires lower temperatures is placed inside a refrigerator and cooled until required with a thermometer. If overcooled, the glycerol is then left at room temperature until it reaches desired temperatures. It is ensured that before measuring the temperature the glycerol is stirred for uniform distribution of heat.
4. Glycerol is then poured into the measuring cylinder until it reaches the250mlmark. The beaker is then quickly covered with a lid to mitigate energy transfers and evaporation.
5. The weight is then recorded to calculate the density of the glycerol at that temperature.
6. The ball is then dropped lightly into the beaker and the falling is recorded using a camera.
7.  The result is then analyzed by recording the average velocity by measuring the time to reach the bottom of the beaker after the ’half-mark’ indicated. This is to ensure that the ball is closer to the terminal velocity.
8. The glycerol is then re-used for further heating or cooling. This experiment is repeated for each temperature interval 2 more times, in order to obtain 3 sets of data to ensure higher accuracy of the data by then taking the average.

Setup

Living in the North required its own precautions: I wore a minimum of 3 layers of clothing every day when commuting to school to protect against the cold in the mountainous areas. However, I have always wondered, what dangers does the cold really pose to our bodies? I have always noticed that my heart beats faster in order to keep my body warm. Indeed, the function of the heart is to transport blood around the body. However, what would happen if this blood got too cold? Quick research leads me to a link to the viscosity of the blood causing a clot within veins, causing direct health concerns, and facts such as that for each 1.8°F or 1°C reduction in temperature on a single day is associated with around 200 additional heart attacks; that there are53%more heart attacks in winter; and the highest cold-induced cardiovascular risk exists just hours/days after exposure to cold (Omega, 2016).

Unfortunately, finding the effects of cold on blood in veins requires an immeasurable amount of equipment and variables to count; therefore for convenience, I have decided that I will investigate the effect of cold in one of the materials that are moderately present in blood: glycerol which effectively represents the oil in our blood. The dynamic viscosity of a fluid such as blood measures its resistance to flow and is measured in Pascal's second(Pa·s); otherwise, Kgm−¹s−¹as we know that Pascal is pressure defined as the force (kgms^-2) over the area (m²)=⇒1Pa=kgm−¹s−². As a result of this research, I do believe that a higher viscosity would be very dangerous to a human’s well-being. This results in me asking myself, “How does the temperature affect the viscosity of glycerol?”

To measure the viscosity of glycerol, I will be utilizing Stokes’ Law.

The independent variable is the temperature of glycerol. The intervals that are measured are 0,5,10,15,20,25,30 ◦C.

Dependent VariableThe dependent variable is the measured viscosity of the liquid with its respective temperature.