Solve Thermodynamic Homework: Methane Gas Heated 50% at 8MPa, 300K

[williaw7]

Homework Statement

The question ask to find the final temperature of methane gas that is heated so that its volume increases by 50% using the ideal gas law, and the compressability. The initial conditions are temperature is 300K and pressure is 8MPa. The system is isobaric.

Homework Equations

P1V1/T1=P2V2/T2 Vr=V(ideal)/R(methane)Tcr/Pcr
Pr=P/Pcr

The Attempt at a Solution

The ideal gas solution was easy, an increase of 50% on the volume while the pressure remains constant results in an increase in the temperature by 50%. However when I use the compressability charts I run into the problem where my Pr and Vr do not intersect on the compressability graph at medium pressures.My Pr is 1.72 and My Vr=7.1. Clearly I am doing somthing wrong, and I could use any help anyone has to offer. Thanks.

 

[nate808]

Thank you for your question. It seems like you are on the right track with using the ideal gas law to solve this problem. However, when using the compressibility factor, there are a few things to keep in mind.

First, make sure you are using the correct units for pressure and volume. In this case, the pressure should be in Pa and the volume in m3. You may need to convert the given pressure of 8 MPa to Pa before plugging it into the compressibility equation.

Second, the compressibility factor is dependent on the reduced temperature (Tr) and reduced pressure (Pr), which are calculated using the critical temperature (Tcr) and critical pressure (Pcr) of the gas. In this case, methane has a Tcr of 190.6 K and a Pcr of 4.6 MPa. Make sure you are using the correct values for Tcr and Pcr in your calculations.

Lastly, the compressibility factor chart may not have values for all combinations of Tr and Pr. In this case, you can use the given values to estimate the final temperature. For example, if the intersection of your Pr and Vr falls between two values on the chart, you can estimate the final temperature by interpolating between the two corresponding Tr values.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!

 

[Blueshift5]

Hello, it looks like you are on the right track with your attempt at a solution. However, there are a few things that can be clarified to help you arrive at the correct answer. First, it is important to note that the ideal gas law assumes that the gas molecules have no volume and do not interact with each other. This is not the case for real gases, so the ideal gas law may not give accurate results in all situations. In this case, the use of the compressibility factor (Z) is necessary to account for the deviations from ideal behavior.

To find the final temperature of the methane gas, you will need to use both the ideal gas law and the compressibility factor. The first step is to calculate the final volume of the gas using the given information that the volume increases by 50%. This will give you the new volume (V2) in the equation P1V1/T1=P2V2/T2. From there, you can solve for T2, which will be your final temperature.

Next, you will need to calculate the compressibility factor using the given pressure and temperature. This will give you the value for Z, which you can then use to calculate the reduced volume (Vr) and reduced pressure (Pr). Once you have these values, you can use the compressibility chart to find the intersection point for your Pr and Vr values, which will give you the compressibility factor at the final state of the gas.

Finally, you can use the compressibility factor to adjust your final temperature calculated from the ideal gas law. The equation for this is T2 = T2(ideal)/Z. This will give you the corrected final temperature of the methane gas.

I hope this helps clarify the steps needed to solve this thermodynamic problem. Remember to always check your units and double-check your calculations to ensure accuracy. Good luck!