Lab 4: First Law of Thermodynamics and Kinetic Theory of Gas

     We started the day with a quiz about temperature, heat and power. Then we did an experiment regarding the work done by an expanding gas.

This graph explains the work you done while eating a sandwich.

Moving the piston to hot water causes the syringe to go up because the gas molecules experience a change in kinetic energy, so the gas molecules move faster, and if put into cold water, the syringe will eventually go down. Professor Mason also constraint the syringe to move so that the temperature increases, which made the syringe expand upwards in an instant.

This is our prediction when the piston is set inside hot water.

     First law of thermodynamics 

This is our definition of the first law to a 7 year old. Also we said that sleeping could be an example when work is negligible, and walking slowly when the heat is negligible.

Here is a problem that consist of conservation of energy. First we find the work done on a copper bar by the surrounding atmosphere pressure.

This is a molecular dynamic applet. With this applet we observed that an increase in temperature and pressure causes an increase in kinetic energy of the atoms. Also when there is only one atom, the pressure will be zero; however, if there is collision between the walls, there is pressure.

     We express the velocity in 2D as the change in distance over time, and in 3D as the square root of Vx^2 + Vy^2 + Vz^2 in 3D, also as 3Vx^2 since the velocity in all directions are the same.

     Taking the equation F= delta p/ delta t, we rewrite the equation of the force done by the wall from a collision to be (2mv)/delta t. Through some simplifications our final equation result in (mv^2)/x.

     Now, using the equation P=F/A, and replacing the (mvx^2)/x for the force, and area as x^2, we get P = (mvx^2)/x^3. Then, the question ask, what if there were N molecules in the box. We can replace x^3 as Volume, then we get P = (Nmvx^2)/V. Now we were given that vx^2 = v^2tot / 3. Our final answer is P =  (Nmvx^2)/3V which is the same as P = 2NEkinetic / 3V. In addition, using the idea gas law equation PV = NkT together with our last equation, we get VRMS= square root of (3kBT/m).

We also talked about Isothermal and Adiabatic processes for an ideal gas. In the Isothermal process, the change in temperature is zero, which leads the change in internal energy to be 0 whereas in the Adiabatic process, the heat equals zero.

Using the first law of thermodynamics we proved the formula for Adiabatic expansions. Also, with the ideal gas law, we proved that the initial temperature and volume is the same as the final temperature and volume.

     Finally we did an experiment with a fire syringe. The idea was to mimic the Adiabatic process, where there is no heat exchange with the surroundings in order to create fire with the rapid compression of air.

First we measured the initial and final length, and the inner diameter in order to calculate the initial and final volume of the fire syringe. We also measured the room temperature using an app in our phones.

Then, we used the formula Ti^(3/2)Vi = Tf^(3/2)Vf   to calculate the temperature required for the cotton to ignite. Our temperature was 1579K.

In this video we can see the cotton ignites after several tries.