How to Find the Work of a Vertical Piston-Cylinder Assembly

Thermodynamics is the study between energy and entropy and it is used by engineers for a variety of designs on a daily basis. These include; air conditioners and refrigerators, turbo chargers and superchargers in automobile engines, steam turbines in power generation plants, and jet engines used in aircraft. A part of these systems are piston-cylinder assemblies, which engineers will study to find the work being done during this process so, they know how efficient it will be in an engine or power plant.

This Instructable will help you learn how to find the work during this process for heating ammonia at a constant pressure. The ammonia will be in a closed system, which is the exchange of energy as work or heat with the surroundings. In order to understand this Instructable beyond the basics requires an engineering or physics background or having studied thermodynamics.

To complete this Instructable you will need the following:

Pencil
Paper
Calculator
Properties of Saturated Ammonia (liquid-vapor): Pressure Table
Properties of Superheated Ammonia Vapor

It should take you about ten to fifteen minutes to complete.

Step 1: Heating Ammonia at Constant Pressure

A vertical piston-cylinder assembly containing 0.23 lb of ammonia, initially a saturated vapor, is placed on a hot plate. Due to the weight of the piston and the surrounding atmospheric pressure, the pressure of the ammonia is 10 lbf/in^2. Heating occurs slowly, and the ammonia expands at constant pressure until the final temperature is 60 degrees Fahrenheit Determine (a) the volume occupied by the ammonia at each state, in ft^3 and (b) the work for the process, in Btu.

Step 2: Find the Volume at Initial Phase

The initial state is a saturated vapor at a pressure of 10 lbf/in^2.

You will use the equation V_1=mv_1. V_1 is the volume, m is the mass, and v_1 is the specific volume. You add a subscript of 1 because it is the initial phase or first phase. Also V_1 will be used in an equation later and is needed to distinguish it from the volume at the final phase.
To find the specific volume you will need to use the properties of saturated ammonia pressure table. Specific volume of a substance is the ratio of the substance's volume to its mass
Find 10 in the first column and then find the specific volume in that row. It should be 25.807 ft^3/lb.
Then you will plug in all the values into the equation and solve for the volume.

Step 3: Find the Volume at Final Phase

The final state is a superheated vapor at a pressure of 10 lbf/in^2 and temperature of 60 degrees Fahrenheit.

You will use the equation V_2=mv_2. V_2 is the volume, m is the mass, and v_2 is the specific volume.
To find the specific volume you will need to use the properties of superheated ammonia vapor table.
Follow the steps as seen in step two to find the volume at the final phase.

Step 4: Determine the Work

Now you can determine the work of the process.

When the pressure is not constant you would normally take the integral between volume one and two of the pressure in respect to v. However, since this is constant pressure the equation you will use is p(V_2-V_1).
Now you will plug in the values you found earlier.
Since the units need to be converted you will first convert it from inches to feet and then from ft*lbf to Btu.
The answer is -4.131 Btu.

Step 5: Review and Additional Help

Now you can find the work in a piston cylinder with constant pressure.

Here is a video attached for you to watch and give you more understanding of piston cylinders in thermodynamics. There are also a lot more videos and links online that can provide additional information on the topic and help you solve more problems.