3/27/2015 electric dipola and electric flux

The electric filed between 2 opposite charged plate that parallel to each other is some straight line parallel to each other and pointing from positive to negative. When a charged particle enters the system with an intial velocity, electric force will be applied on it and makes its motion like a projectile motion.

We define electric dipola moment as a vector that directed from one particle to another particle. This will be used to solve torque and work done by electric force later.

When there is a system inside the electric field that is made up by 2 differently charged particles, the net force is 0, but the net torque isn't 0, which will cause rotation. Next, we derived that torque is cross product of electric dipola moment and elextric field, P X E, and work done by electric force is dot product of -P and E.

This is the prediction of a minimum work phyton program output. We want to use this program to display the electric field of the system consisted of 2 differently charged particles. Apparently, this is not the correct answer, thus we will modify the program.

This is the prediction we made for the electric field of the system. The red arrow is the total electric field at each point on the circle.

After we modify the program, it shows the distribution of electric field as a 2D distribution. However, we want to show it in a real 3D space, and we continue to modify it. Above all, the output matches our prediction.

After modifying the program, we make it show the distribution of electric field in 3D space, and it matches our prediction, too.

We apply the definition of electric field line. The more electric field line it has in a certain area, the stronger the electric field there is. We then use it to work with electric flux.

Electric flux is how many electric lines pass through the surface. The definition is the dot product between electric field and area. It is also the integral ( EdA ). When the angle between the surface and electric field is 90 degrees, the flux will be 0. Since it is a dot product, it has no direction.

In a cubic, we calculate the electric flux on each surface. When the electric field is parallel to the surface, the electric flux is 0. When electric is normal to the surface, the electric flux maxmizes.

3/25/2015 electric field

From gravity field to electric field, we define some properties that an electric field will have. We think that the electric is caused by charging the particles and its magnitude is influenced by the charge and distance between the particles. What is more, it is a vector.

We list some necessary steps to figure out an electric field. Notice that we eventually want to write an electric field in a unit vector form to label its direction since it is a vector. In the end, we write a more general form to calculate electric field including its direction as well as magnitude.

Before we write the python program, we firstly predict what will the minimum work source code will generate and draw it on the white board. This graph shows the xyz plane and where the original point will be.

This is the sample run of the program. It shows one electric field line and its direction.

By modifying the source code, the program will finally be able to show some electric field line in a 3D view. Since we make it have positive charges, the direction of those electric line is pointing away from the particle.

We modify the code again so that it will show us the magnitude of electric field as well as just showing their direction, and we record it on the white board.

This is one sample calculation to calculate the electric field at a certain point in a system that is made up by more than one particle charges. We express it in unit vector form.

Making it more complicated, but the steps the electric field is still same. By applying the formula, the only thing we need to be careful is that we need to draw the electric field direction right, make it have the correct direction that the vector is pointing to on x and y components.

We then calculated electric field along and from a uniformly charged. We applied calculus and integration to solve it. This is the data calculated on instrustor's laptop.

Same problem, this picture is what we calculated on our laptop. The result has differences comparing to instructor's calculation, and the picture i take is not clear enough.

We derive a more general form of calculation for the electric field by integration for non-uniform distribution charged particles or system. It is similiar to calculate the moment of inertia. To express dQ, we apply line charge density, area charge density and volum charge density.

Entropy(last day of thermal) 3/17/2015

We derive a formula of entropy, and we found that it is the ratio of the heat and temperature. Next, we listed something in our classroom that increasing entropy, but remain a constant thermal energy. They all have a similarity which is they are all experiencing phase change.

As well as regular p-v diagrams, we draw a T-S diagram to describe the relationship between temperature and entropy of adianadic, isothermal, isovolume and isobaric process.

We have introduced a new kind of engine, Stirling engine. The way it works is due to the difference of temperature of the bottom and top, the air inside the engine and does work, which makes the engine works.

In order to compare the efficiency of the Stirling engine and Carnot engine, we calculate a efficiency of one cycle of a Carnot engine. We use the formula: e = 1-Qc/Qh

We are introduced a new concept, coefficient of performance. The best refrigeration cycle is one that removes the greatest amount of heat  from the inside of the refrigerator for the least expenditure of mechanical work,  The relevant ratio is coefficient of performane. The larger this ratio, the better the refrigerator. 

We are doing a regular heat transfer problem of a heat engine. At this point, we just directly applied the formula and pv = nRT, as well as Q = cmT to solve the Qh.

Later, by giving those amounts of data, we directly apply the formula, we are able to solve the efficiency of the heat engine.

At this problem, we are given that the change of entropy is 0 during the process, thus we just directly applied the formula, change of entropy = Intergral ( dQ/T ) = Intergral ( cmdT/T ) = cmln(Tf/Ti) = 0. Then, after pluging the number, we were able to solve the final temperature.

This is a refrigerator problem. The general idea is almost same to solve a heat engine problem. However, there is a key point we need to be  careful which is the heat we get by multiply COP is Qc not Qc.  

This is the last experiment. By making some bubble and ignite them, we observe a great reaction from the bubble. The conclusion we can draw is as entropy increasing, the system gets less stable.

Carnot engine and viechel egine

We observed that the difference of temperature can produce electric, which means heat/thermal energy can transfer to electric energy.

This is the prediction that we switch the temperature of the two bars and obserserve what will happen. The result is that it still produces electric energy, but rotates with opposite direction. 

We derive the molar capacity when the volume remains constant.

We derive the molar capacity when the pressure remains constant.

In the adiabatic process, we express the product of temperature change and mold amount in terms of change of pressure and the 2 heat capacity.

we got a relationship between pressure, volume, change of pressure, change of volume and the 2 heat capacity.

By set up the integral, we got a formula of work done by a system which is only applied in adiabatic process, and we used it to solve a question.

We have a engine cycle, by the given process and the formula we have, we can have the heat change, internal energy change and work done of each process. In the end, we can solve for the efficiency.

We are shown a model of how modern engines works.

In the end, we list some methods to improve the efficiency of engines 

law of thermal dynamic

We use this applet to find the relation between temperature, pressure and volume when one of them remains constant.

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We draw conclusion that thermal dynamic can be described with pressure, volume and temperature.

We define some other thermal transfer process, which are isobaric( pressure remains constant ) and isovolume ( volume remains constant). and solve a simple problem.

We draw the curve for each thermal transfer process: isothermal, adiabatic, isobaric and isovolume.

We watch a video that when we use a heat gun to heat a string, is it gonna compress or expand. This is our prediction and the actual result. This is because of the material of the string, and this is used to upload and unload the can in our real life.

We define 4 process that the can lift engine works.

We derive the expression of the heat engine.

In the P-V diagram circle, The are enclosed by the graph is the total work done in the system. When we solve such a problem, we use W = intergral of PdV. The only thing is we need to be careful which element is constant during each process.

This is a pv diagram of a heat engine. based on the pressure and volume of each process, we can find internal energy, change of internal energy, work done by the engine and the heat gain or lose from the heat engine.

During this experiment, we record temperature, pressure and volume to make another pv diagram to figure out the change of heat, work done by system and change of internal energy.

This is the pv diagram we got from logo pro.

Based on the pv diagram and w = intergral of vat, we could find the change of internal energy, work done by the system, and heat change during each process. By Ein = 1.5PV, we could find the internal energy at the points A, B, C, and D