(9/9/14) Work and the First Law of Thermodynamics

In this lab, we are covering over work, heat, and the internal energy of the system, and how the idea of the First Law of Thermodynamics was formed off of these three forms of energy

Relating Work and Pressure Mathematically:

A revisit set-up from the last lab

We first started this lab by bringing up the heated syringe lab activity we used to find the relationship between volume vs temperature. This time, however, we asked what occurs to the gas if we were to keep the plunger fixed. How would the gas react to keep itself at equilibrium

A demonstration of how to keep the plunger at bay.

We find out that in order for the plunger to stay at a fixed distance, that work has to be applied onto the plunger by an external factor (in this case, Prof Mason's index finger) in order for the plunger to stay fixed. Of course, when the index finger is removed, so is the external work done to the plunger, and it is free to move up, as it should. 

Giving this term of work a mathematical definition

We moved straight along to give a definitive definition of work, which we find out to be the integral of Fdr, where F is the force, and dr is the differential of the distance moved.
To take the definition a bit further, we took the idea of Force, which is Pressure x Area, and substituted it for force. Realizing that Adr (which we made dx to give the term familiarity) is just dV (area being meters squared, and dx being meters), we then derive the term that work is equal to the integral of pressure by the change in volume

Finding Work

 A two part problem, testing our knowledge of the First Law of Themodynamics
The first part gives us mass, ΔT, and pressure, and we are to find the work applied, in which case we first needed the final pressure, which was unknown as well.

The second part of the problem asked us to first find the Q (heat), and once we found Q, we then find the ΔU (internal energy) of the system.
Finding Q was just the process of Q=mcΔT
Finding ΔU used the idea of the First Law of Thermodynamics, since we have now both Q and W

2D Molecular Motion and Pressure:

We started this lab by using a 2D simulation of a diatomic atom at near absolute zero, and steadily increased the temperature to see what occurs. 

Atoms in motion computer simluation

We find out quickly that as the temperature reached to a certain point, the London Dispersion Force that was holding them apart broke, and the diatomic particle became two mono-atomic particles, bouncing faster and creating more work and pressure, the more that the temperature was increased in the system.

Larger amount of atoms in motion computer simulator

We took that idea to the next level by adding more atoms to the system, ideally colliding in a perfectly elastic collision, thereb increasing the pressure, and once again increasing the work of the system, as the temperature was added in. Additionally, the path in which the atoms take became harder to notice, as more atoms were added to the system.

(Interestingly enough, the simulation crash after a while, unable to handle to handle it)

We took this idea, expanded it to a 3D situation, and tried to solve for various terms.

Finding our velocity component, and their Vtotal

We were first asked to find the equations needed to calculate the x,y, and z components of velocity using X,Y, and Z and their time components.
Once we found these equations, we then needed to find the Vtotal in terms of the x,y, and z components.
While answering this question, we assumed that Vx=Vy=Vz, and was able to simplify the final results to be easier to work with. 

Finding time 

We were then asked to find Δt in the x-direction, which is the amount of time the molecule to go from the left wall, bounce off the right wall, and head back to the left wall
Since we noticed that the movements of the ball is just Δt=2Δtx, we substituted that in to Δt

Finding amount of force exerted 

We can then, using the idea of F=Δp/Δt (the true Newton's Second Law) and the equation we used to find time, to find the amount of force exerted on each collision

Expressing Fx

Once we had an idea of the amount of force exerted, we can then substitute the expression we had to find the velocity of each component (the very first equation we derived) in order to find an expression just for Fx

Expressing Pressure

We then took the idea of a cubical box with the length=width=height, making the volume V= X^3. By understanding the concept of pressure= force/area, we can then use it to express the pressure on the wall of this cubical box, caused by Fx and due to a single atom.

Two different expressions of Pressure (due to Fx and P)

However, if we wanted the expression of Fx due to a N amount of terms Vtotal, we need to add in the idea that V=x^3 and understand the equation of vtot that we calculated early in the system ([vtot]^2= 3 vx^2] and can rewrite it to find pressure as function of vtot and V(pressure)
Additionally, understanding that mvtot^2 is just kinetic energy, we can again rewrite the equation as a function of Kinetic Energy

Gas Law and Kinetic Energy
Understanding the idea of the ideal gas law in terms of PV = NkbT, we also understand the following relationships
As the volume increases - the pressure decreases
As the number of particles increases - the pressure increases

Microscopic Definition of T

Relationships between N,P, and V to kinetic energy (right side)
Relating <Ekin> and T (left side)

We can take the ideal gas law, and show that PV=2/3N<Ekin> (as shown on the left side).
Additionally, by sing the derived form of Ekin and T, we can then play around with the equation to obtain the vrms, or the root mean square velocity of molecules.







Isothermal Compression of Gas

Equation of Isothermal compression

We next learned about isothermal and adiabetic  compression of gas
In this first picture, we show that Eint = 3/2NkbΔT
We then can understand that in an isothermal compression, temperature remains constant throughout. Using the ideal gas law, we can state that pV=nRT, and since nRT is a constant, we learn that pV= constant, and p1V1=p2V2
Additionally, since in an isothermal compression, there is no change in internal energy, that heat and work must them be equal to each other



Adiabetic Compression of Gas

In an Adiabetic Compression, however, pressure is constant. With pressure being constant, we then find that the heat must then be zero, and that ΔE = -W. By reiterating that ΔE = 3/2NkbΔT and that work equals to -pΔV, we can then play with the equation, and with a little bit of integration, create the equations that expresses adiabetic compression of a gas.
Additionally, we must understand that the equation for an adiabetic equation shown here is only in cases of monotonic gases, and in diatomic gases require an extra two dimensions of freedom, thereby increasing from 3/2 to 5/2 


The Fire Syringe - Fahrenheit 451:

Our fire syringe and caliper needed for the experiment

In our last experiment, we were allow to spontaneously combust a piece of paper (or in our case cotton ball) using a fire syringe (which uses an adiabetic compression when done fast enough) and compare it to the "flash-point" of paper, which is 451°F

Our calculations and prediction for the combustion of the cotton ball

Before allowed to do the experiment, we needed to first calculate, using the Δh, the ΔV and the ΔT, the temperature that we should reach, and whether or not we should reach the flash-point

With our calculations, we calculated our temperature to be about 752K (error on my part of the °C) which is about 900°F, over double of how much we need to reach the flash-point

Our video of the activity
(Due to the sudden spark, my camera went wacko)

Although hard to see due to the video's sudden light issues, we do in fact create a spark with the cotton ball.
Additionally, to ensure that our experiment was a success (and to try to capture a better video) we attempted this experiment twice more, obtaining a spark (and a bad video) each time.












Conclusion:
Overall, we were able to successfully progress ourselves from the ideal gas law that we experimented from the last lab, into adiabetic and isothermal compression, through the usage of the Ideal Gas Law, and the First Law of Thermodynamics. We learned how to express the ideal gas law in the form of 3/2NkbT, which we then used to understand ΔE, helping understand the First Law of Thermodynamics, and ultimately leading to isothermal and adiabetic compressions (and causing cotton balls to spontaneously combust as well).

(09/04/14) Gas Law and First Law of Thermodynamics

Within this lab, we learned about the relationship between volume, pressure, and temperature, and derived the ideal gas law.

The picture of our can theory

In our first portion of the class, we theorized what would occur to a soda can with 13mL of water at 100°C, if it were to be placed in a container of water at room temperature

We predicted that the can would quickly implode

The video of the experimentation

End Result of our lab

We were able to correctly predict that due to the gas particles overtaking the can, the can as a result will quickly implode

Our depiction of the relationship between force and momentum

During the class, we were asked to find the correlation between force and momentum. Using Newton's Second Law and the equation for momentum, we were able to successfully find a relationship, that force and momentum are directly proportional to each other

Unfortunately, I do not have a pic of me doing the experimentation
But look! A manometer

We then entered our first class lab, using a manometer to measure gas pressure. By blowing on one end of the tube after keeping the water at equilibrium, and measure the difference in the height, we were able to successfully find the gas pressure

Calculations of the manometer, as well as finding pressure 

Our predictions of the three graphs

The next part of the lab asked us to make theories of three different types of graphs, pressure vs. temperature, volume vs temperature and pressure vs volume, as we went through each of these experiments to see whether or not these predictions holds true or not.

Forgot to take a real life picture of the apparatus 

Our first graph that we proved was the pressure vs volume temperature. We did so by using loggerpro, a pressure sensor, and a 20cc syringe. By setting the Logger-pro to collect data per certain points(event mode) we were able to graph the pressure using the volume as points. 

Not the cleanest line, but it shows an inverse
proportion relationship

The graph that appeared, although not as clear as we would like, shows that pressure and volume has an inversely proportional relationship, which is just about what we predicted in our theory

The speech of the P v T graph

The second portion of the experiment involved finding the relationship between pressure and temperature. By using the pressure sensor and hot water + ice, we can see the change of temperature, and also examine how the pressure changed along with it. 

Yet another messy graph

Although the graph is a bit messy, it is showing what should be a straight line, which proves that pressure and temperature are directly proportional to each other. Once again, our prediction is correct

We now hit into the final portion of this experiment, volume vs temperature by using a near-frictionless syringe.This lab involved using using three different containers of water in different temperature, one at about 70°C, one at room temp, and one at 0°C. 

The video for the volume vs temperature experiment

A much cleaner graph

As the (beautiful) graph shows a (beautifully) straight line, we once again prove to be correct in our prediction that as temperature changes, volume changes as a direct proportion. 

The idea is the the two graphs reshows the inverse proportion
between pressure and volume (while temperature is constant) 

We then took the equations from both the pressure vs temperature and the volume vs temperature, and created a relationship with each other

A class problem, involving finding pressure of a diving bell after it leaves the surface

The answer(s) to the the complex diving bell question

Our theory about what should occur to the balloon

Our next portion of the lab required two parts, but asked the same question; what would happen if you increase, then decrease the air in a vaccum environment when there are the following inside:
1) A balloon
2) Marshmellows

Our theory on what should occur to the marshmellow

Balloon inside vacuum

The first video shows what occurs to the balloon. and how it went from big to small, smaller than its original size to keep note, following our theory

Marshmallow buddies in the vaccuum environment

Our second videos shows what occurs to the marshmallows after air goes in, then out. My prediction was that it should be a slightly bigger size, which was proven to be incorrect

Latent Heat Lab

Within this lab, we did an experiment to find the latent heat of fusion and vaporization of water


To begin the lab, we started by theorizing what would happen if you expand a ring using heat

Our answer stats that the ring should theoretically expand infinitely

We then questioned what would occur to a bar of two differnet metal, Brass and Invar (knowing the the expansion of Invar is less than the expansion of Brass), should we heat it on each side of the metal

We theorized that when you heat the Invar side, the Brass side will bend, and vice-versa with heating the Brass side

Within the video, Prof Mason proves our theory to be wrong, showing that no matter which side you heat the metal to, it will always curve to the Invar side

Same concept as the heating, except instead of heating the metal, we cooled it to see if anything different changed.

Our next lab required this extensive setup of a steamer, a steel pole, and a wheel attached to the pole, spinning whenever the pole was expanding due to heat. Given the initial length, the initial and final temperatrure, and the diameter of the wheel, we were to find the constant (in 1/°C) of the pole, using the linear expansion formula ΔL=LoαΔT, where α is the constant we are calculating for

By converting the ΔL to its angular counterpart, rΔθ, we were able to calculate the α constant to about 1.2e-10 1/°C

We then moved on to the phases of water, and how they looked like when graphed experimentally. From chemistry, we were taught that the graphs are clean, straight, and linear.

The reality of phase changes

In reality, the curve looks a bit more parabolic than straight. Although the picture doesn't nessarily show it, until it hit a constant temperature at about 100°C, it rose and decline, which is not typical of what you would see in a chemistry book





Once we understood the truth about phase changes, we then moved on to calculating the heat of vaporization and fusion via experimentation. Here in this lab, there were no specific instructions on what to do, so instead, using the hints that Prof. Mason had kindly provided.

Our own ideas of how to do the lab

Using 100g of water and ice to make sure that there was just enough water for the immersion to stay submerse, while not taking too long to boil, we decided to use the following:

• Use paper towels in order to dry the ice
• By using a beaker, we can measure about the same amount of water as ice (since water is 1g/cc) and used the scale to measure the mass of the ice
• Place the water and beaker in a cold environment for 5 mins to let it reach to around 0°C (used the ice container along with a thermometer for this step)
• To find the Joules used, we can find the amount of power that the immersion released, and multiply it by its time.

To find the mass of the steam that escaped, we required the heat of vaporization, and can convert the equation as to look for the mass of the steam

Our graph, containing, with great accuracy, our specific heat of  water

Calculating the latent heat of fusion and of vaporization through experimentation