The Otto Engine and The Carnot Engine

Purpose:  In this lab, we focus on two major engines, the otto engine and the carnot engine. We will differentiate the two and find which which engine is best for modern day use and why it is best today.

Hot and Cold Reserviors

We start off by looking at how a hot a cold reservoir generates electricity

The energy generated from the hot and cold reservoirs leads to work being done on the disk.

The video demonstrates a live action of what was described in the two pictures above. We see that in an engine, the hot reservoir is used to instill energy into the engine, which it then does work, and uses the cold reservoir to release any unused energy.

We do the same type of experiment but switch the orientation of the hot and cold reservoirs. Apparently, the orientation of the reservoirs dictates on which direction the disk spins. This discovery astounds the entire class. We see that the only thing we change is the heat flow. So, we can then say that corresponding to the previous experiment, the disk spins the same direction. The change in direction of the heat flow will then change the direction that the work does.

A Simple Model of a Refrigerator

The next experiment demonstrates how to make a simple refrigerator using electricity.

As Professor Mason says, "we can use electricity to create a temperature difference" and this allows us to utilize the cool side to refrigerate something.

Our group draws a diagram of the metal that cools and heats. Heat flows from one side to the other, making one side cold and the other side hot. This is done using electricity.

Deriving Cv

Using the definition of the change of internal energy, we derived an expression for molar specific heat capacity at constant volume in terms of R.

Deriving Cp

Next, we used the definition of 1 law of thermodynamics to help derive the molar heat capacity at constant pressure. We find that this value is just the Cv plus R.

Taking a Look At the Change In Volume and Pressure

Using the definition of the derivative, we create a derivation of moles times the change in temperature and find it is the product rule of pressure and volume divided by the difference in molar heat capacity at constant pressure and constant volume.

Setting Up a Differential Equation for Pressure And Volume

We look at the previous derivation and take it a step further, setting up a differential equation in which we solve. We solve the differential equation to get a relationship between initial pressure and volume to final pressure and volume in an adiabatic process

We continue even further with the derivation to find a relationship in an adiabatic process using temperature. We are able to use this by substituting pressure.

A New Definition For Work

Using the definition for work using pressure and volume, we created a new definition for work using the newly derived relationship between pressure and volume for an adiabatic process. This, then, allows us to find the work in an adiabatic process.

Example Problems For an Adiabatic Process

Using the newly derived definition for work, we are able to calculated the work done on a process with the given values.

The Carnot Engine

We solve a Carnot cycle. This cycle contains the isothermal and adiabatic processes. Using our newly derived equations, we are able to quickly find the values for heat, work, and change in internal energy. Notice the the heat in certain processes is zero. This defies the real capabilities of the physical world, as there is no such way to create a reversible process like that of a Carnot engine. Some heat is lost.

The Efficiency of a Carnot Cycle

Continuing from the previous problem, we then have to find the efficiency. we found that the ratio between cold and hot heat is equal to the ratio of the cold and hot temperature of the reservoirs. WE concluded that in order to gain the best efficiency, we have to either raise the temperature of the hot reservoir or lower the temperature of the cold reservoir; or do both.

Visual Representation of a Otto Engine

Professor Mason pulls out a visual representation of a piston used in otto engines.

We see that the piston continuously moves up and down, doing work but only goes through combustion every other compression. This is the same type of simulation done previously in a different lab with creating fire. Using the same ideas, the piston creates energy using the combustion and pushes the piston down doing work. the piston then pushes back up releasing the unused heat into the cold reservoir and continues the cycle over and over again.

On our board, we've written down ways we thought could improved the output of work done by the engine.

Conclusion:  We have looked at the significance of hot an cold reservoirs and how they can be used to produce energy. The same can be seen in reverse, as we used electricity to create our own hot and cold reservoirs and utilize the cold reservoir for refrigeration. These ideas were important for discussing the Carnot and Otto engines. We see that in a Carnot engine, we can find the maximum efficiency of an engine with hot and cold reservoirs since the process is reversible. But the theory of a reversible process is merely a fairy tale used to gauge the maximum possible efficiency of an engine with the same hot and cold reservoirs, such as the otto engine.