Work, Energy, and Heat

This picture is a review of the quiz we took at the start of class.

The above 3 pictures show Professor Mason submerging a beaker in water of different temperatures. The beaker of air is connected to a glass tubing which shows a change in volume.

Work equals the integral of Pressure times the change in volume. The kinetic energy increases with the increase in temperature which causes the volume to increase.

In this picture we we show that Work is the change of energy in the system. Heat in the system is equal to internal energy which is the change of internal energy which is equal to the heat in the system minus the Work. We also tried describing this to a child, and we didn't do too well, but Professor Mason gave us an example of how eating candy can make children hyper.

The applet above shows how molecules react when there is a change in Kinetic Energy. It also shows that the pressure and temperature are reliant upon the velocity.

In this picture we have real life examples of a change in energy being reliant upon either heat alone or work alone. A hot steak sitting on a plate was our example of a change in internal energy relying only on heat. A balloon losing air over time was our example of work causing the change in energy.

The picture above shows how we found the Work done by first finding the change in volume of a cube in a 30 degree Celcius change in temperature.

In the picture above we derive a Force equation based on pressure and a change in time.

Above we derived a function of pressure in terms of volume.

We found that the root mean squared velocity is equal to the root of 3 times the Boltzmann constant times change in temperature over mass.

The above picture shows the details on an isothermal process and an adulate process. 

The above video and white board picture is the experiment we conducted in class. It is an example of an adulate process since it occurs quickly and there is no heat energy.

Here are the questions regarding the last experiment in the lab manual, our calculations in class match up with the ones in the book.

Pressure vs. Temperature and Volume

The picture above shows what we thought would happen if a heated can was introduced to a container of cold water. We assumed it would implode since the little water inside the can would expand with heat, but would rapidly shrink once placed in the ice water.

The video above shows what happens when a heated can is dropped into a beaker of cold water, it implodes.

We assumed that the experiment would run similarly when the can was placed top end down, just to a lesser extent.

The video above shows what happens when a similar can is placed top end down into a beaker of cold water. Since the can was heated, the the volume of air was displaced out of the top, when placed top end down into the water, the volume has to be replaced, but since the top end is down it sucks in the water. Also, at the end of the video, we have visual evidence that Harrison is habitually late.

This picture shows the units of pressure on the left and how we calculate air pressure at sea level.

This picture shows what we thought the graph of the function of pressure in terms of volume would look like

We performed an experiment which measured pressure through a syringe. Late Harrison pushed the syringe in and every 2 cm^3 we took a reading. This is a graph of that experiment, pressure as a function of volume. We did an inverse fit on it. p = A/V + B. This fit was better than just the standard inverse, p = A/V, since the B adds a little wiggle room which gives it a more accurate curve to match the graph.

This picture explains the experiment that we performed and also shows what the units of A would be.

Professor Mason heats the container to show the relationship between pressure and temperature.

My prediction of what the graph of the function of pressure in terms of temperature would look like. Sandy originally drew a straight line but I assumed it was curved so we went with that.

The actual function of pressure in terms of temperature. So our prediction would have been correct if I had left well enough alone, but that's not what Bob would do.

The beaker of air is placed in another beaker filled with hot water. This was one part of the experiment showing the relationship between volume and temperature.

Another part of the experiment involved placing the beaker of air into a beaker filled with ice water. 

The beaker of air was also placed in a room temperate beaker of water.

The above picture shows the graph of the relationship between temperature and volume.

The Boltzmann Constant is equal to the ideal-gas constant divided by Avogadro's Number. Rather than relating pressure and volume on a per mole basis, this constant relates these on a per molecule basis, and has units of Joules per molecule kelvin

The above two pictures show the diving bell problem. We first determine the pressure that the bell is under by equating it with the pressure of the water around it. Then we use the ideal gas law to determine the height at which the water raised.

Our assumption of what would happen with the balloon and marshmallows in the vacuum. Both would get larger as pressure goes down and both would return to normal size after.

The balloon before the air has been sucked out of the vacuum.

Most of the air has been removed from the the vacuum, and as a result the volume of the air inside of the balloon has greatly increased, causing the balloon to inflate.

The above picture shows the balloon after air is restored. It has returned to it's normal size.

The picture above shows the marshmallows before the air is sucked out, the one outside is our control group.

When the pressure drops the air inside of the mallows increases in volume causing the marshmallows to greatly expand.

In the picture above we were given the volume, pressure, molecular mass, and temperature of Helium in a balloon. With that information we were able to use the ideal gas law and find the mass of helium present.

Heat, Thermal Expansion and Phase Change

Professor Mason is heating up a metal disc to show that the radius of the disk will expand, allowing a steel ball, which previously would not fit through the gap, to fit through. This shows thermal expansion.

This is a visual representation of the atoms in the metal and their bonds. After heat is applied the bonds expand.

Another picture illustrating the expansion of the metal with heat energy.

A visual representation of linear thermal expansion. It relies on the initial length, material (specific heat), and the initial temperature.

In the picture above, Professor Mason is heating a metal rod composed of a different element on each side. One side is brass and the other is invar. Since brass is more malleable than invar we can see that even when the invar side is heated brass is the material that is effected.

Another picture of Professor Mason heating the metal rod. This time the brass side was heated, and just as above the rod bends toward the invar.

The picture above shows Professor Mason holding the metal rod after submerging it in ice. Since the brass is more malleable we can see that the rod bends toward the brass side, since brass will shrink before invar.

The above picture shows are thoughts on which direction the rod would bend. We assumed correctly since the rod always bent toward the invar, except when it was cooled.

This picture is of the steel rod, prior to the addition of heat. On the right there is a tool which measures the expansion of the rod and to the left there is a tool that introduces hot steam to the rod, causing it to expand.

A closer look at the tool which introduces heat to the metal rod.

The above two pictures are the graphs representing the change in temperature over time on the rod and the angle at which the rod had expanded.

This is our work to attain the alpha of the steel rod from our experiment where steam was introduced to a rod. 

This is the graph of the experiment involving ice water and a heater. A sensor was placed in the water and a student stirred the water, increasing the speed at which the temperature changed. Contrary to what we see in our books, the temperature and phase changes take place at a gradual rate, rather than a slant and flat step we have see in the books.

This is what we expected the graph to look like of the ice melting in the cup. We assumed it would follow a rigid path, just like we see in most textbooks. In the end we were wrong because the change was more gradual.

This picture shows our board after the stirring of the water experiment. Much of the water was lost so we would call that catastrophic error. This picture also shows our work to find the heat of fusion of water in this experiment.

This is our work showing the final temperature of a system where 215 kJ of heat energy are added to a 790 g black of ice at -5 degrees celsius. We checked the energy of the ice going to 0 degrees celsius and the phase change from ice to liquid. There isn't enough energy to completely change so some of the ice remains, meaning the final temp is 0 degrees celsius.

This was our calculation to determine how much water needed to be added to a vessel containing ice at -12 degrees celsius so that all of the water would freeze and the final temp would be 0 degrees celsius. Unfortunately we placed the wrong variable (mass of the ice) in the phase change portion of our equation, since water was undergoing the phase change we should have multiplied that mass by the heat of fusion constant.

The video above shows Daniel blowing into the manometer causing one side of the water to rise while the side close to him descends. This video also confirms what we all expected, Daniel is in fact dumb.

This is our calculation for the pressure which Daniel introduced into our manometer system.

The above picture shows our work for the uncertainty propagation for the coefficient of linear expansion for steel. Our answer was within reason since our uncertainty for alpha was 0.95 x 10^-5 1/C. In the end our final answer was 1.9 x 10^-5 + 0.95 x 10^-5 1/C, well within range of the actual coefficient of linear expansion of steel, which is 1.2 x 10^-5 1/C.