Gas Cycles

The following picture displays the graphs for Volume vs Temp, & Pressure vs Temp for isobaric, isochoric, and isothermal processes.

1. Isobaric processes: one in which the pressure and number of atoms remain constant as the gas volume and temperature change.
2. Isochoric processes: one in which volume and the number of atoms remains the same, while the gas pressure and temperature change.
3. Isothermal processes: one in which temperature and number of atoms remains the same while the gas pressure and volume change.

Here we solved an isobaric problem and solved for the final volume. Since the pressure and atoms are constant we were able to use Charles' Gas Law. When solving gas process problems, we can use the Gas Laws from earlier labs to solve for unknowns. We just have to make sure that the variables changing and the constants coincide with the correct gas law.

As explained previously, we were able to use one the gas laws to solve for the final pressure. Here we used Gay-Lussac's Law.

In this case, we used Boyle's Law to solve for the final pressures.

In this activity, we watched a video showing how a rubber band reacts when heated. Surprisingly, the rubber band shrinks up instead of stretching out.

Because we know that a heated rubber band absorbs energy and releases energy when it is cooled, we can imagine a working system.

Efficiency is defined by work done divided by the heat energy.
100% efficiency is impossible. 

Here we analyzed the work done by a "piston" like apparatus. The piston moved up or down in relation to the temperature and pressure within the cylinder. The next 4 images display the given values provided, apparatus image, and the graph for the gas cycle. 

On the graph below, the givens are displayed and work done for each section is determined.

Calculations for internal energy, heat energy, and work are shown and put into a table. Always put calculations into tables after solving. It is easier to compare findings and sum up net work, newt internal energy and heat energy.

The net work is calculated from the sum of the work calculations from table above.
We also compared this value to the area of the pressure vs volume graph. They were the same.

The pressure inside of a vertical piston can be found using the formula derived below. Since we know that pressure is equal to force per area unit, we were able to substitute the force with mass multiplied by acceleration. Because it is a vertical piston, the acceleration is due to gravity. The area of a cylinder is now substituted for the area variable. After simplifying, we found the pressure equation.

This activity was slightly different. We needed to find the constant number of moles before proceeding. We knew that the gas was air and air is mostly nitrogen, a diatomic gas molecule. So we then found the grams of nitrogen gas used and converted the specific heat capacity of nitrogen from kJ/mol*K to J/g*K.

We then used this info to find the heat energy for each process in the cycle since we also knew the temperature at each point.

Since only the number of moles are constant is this cycle, we were able to use the Ideal Gas Law: PV=nRT. The internal energy is: E=(3/2)nRT. From these two equations, we formulated that E=(3/2)PV. The calculations are as shown.

As previously stated, we should always made tables of final calculations to make comparisons and summations.

Summary:

• The gas cycles we studied have four processes. 
• By using the graphs of pressure vs volume, pressure vs temperature and volume vs temperature, we can determine the type of process performed.
• The four processes studied thus far are:
• isothermal -constant temperature & # of moles
• isobaric -constant pressure & # of moles
• isochoric -constant volume & # of moles
• The net work done in a cycle can be determined by summing up the work from each process or by calculating the area of the pressure vs volume graph.