Kinetic Theory (Fourth Day)

Spring 2015
5th of March's Class

Kinetic Theory

The professor started the class by demonstrating an experiment by showing that expanding air can cause Work Done. He placed a syringe filled with air into a beaker of hot water, and as the temperature within the syringe rises, the volume of air in the syringe expands. As the volume expands, it pushes the syringe outward; as a result the syringe is pushed upward, hence, creating Work Done.

                                                   

As the volume of the air expands, it pushes out the syringe, so the professor put pressure on the syringe to hold it in place to let us understand that there is a relation between pressure and work done.

We then derived that work done can be written as the integration of Pressure and Volume. The image below is the picture that shows how the derivation was done.

Calculation Steps:
- First, we know that Work's basic formula is Force multiplied by Distance.

- Since distance is the change in position, it can be rewritten as the integral of Force with the change in position.

- One of the commonly known formula for finding pressure is Force divided by Area. By singling out Force, we have the formula for Force = Area multiplied by Pressure.

- We substitute the Force in the Work Done's Formula with the newly derived Force's formula.

- Now we have Work Done equals the integration of Pressure multiplied by Area with change in x.

- If we multiplied the Area with the change in x, then we would get the change of Volume.

- Hence we obtained the derived formula that Work Done = Integration of Pressure over the change in Volume.

The professor then used a simulator program in the computer to show us how the gas particles would behave under changing Pressure and Temperature. Although he did not change the volume, he showed us what happens when there was only one particle in the container. He also showed us what happened when the Temperature reach 0 degrees Kelvin, in which the particles does not move at all, becoming rigid.

The professor then wanted us to derivate together with him, an equation that would ultimately leads us to an understanding how the Ideal Gas Law of PV=nRT could relate to Energy. The final form of the equation is shown on the last picture, at (k).

The image above is the next question that he gave us. He wanted us to derivate the formula for Root Mean Square velocity.

The image above shows how our attempt at solving the question. For clarification purpose, the first step taken is shown in the red box, and the final step, which is also the solution is shown in pink box.

After that, he gave the question above to us. The image below is how we attempt to solve it.

As we were not organized when attempting this question, I boxed them to clarify the order of solving. The red box was the first step, then the yellow box, then the pink box.

At the end of the class we did an experiment that shows how pressure can be translated into heat energy, under the condition that the movement must happen in a short period of time.

Since the ignition point for cotton is 528 degrees Kelvin, and according to our calculation the final temperature reached 2860.8 degrees Kelvin, it is no wonder that the cotton would ignite under the circumstances.