A mixture of 4 lbm oxygen and 4 lbm of argon is in an insulated piston cylinder arrangement at 1

A mixture of 4 lbm oxygen and 4 lbm of argon is in an...

Key Concepts

Properties of Gas Mixtures

When dealing with mixtures of gases, the overall behavior can often be modeled by ideal gas relations by appropriately averaging the thermodynamic properties of the individual gases. Concepts such as effective specific heats, gas constants, and ratios of specific heats are used to simplify the analysis of the thermodynamic processes in gas mixtures, allowing the application of standard energy and state equations.

Work in Piston-Cylinder Systems

In piston-cylinder arrangements, work is typically calculated by integrating the pressure with respect to a change in volume. For adiabatic processes, the work done can be determined from the change in internal energy, and it represents the energy required to compress or expand the gas. This concept is essential for evaluating the mechanical energy interactions in such systems.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. In such a process, any change in the internal energy of the system is solely due to work done on or by the system. This concept is fundamental when analyzing insulated piston cylinder devices, where the energy transfer occurs only through mechanical work during compression or expansion.

Ideal Gas Law

The ideal gas law provides the relationship among pressure, volume, temperature, and mass (or number of moles) of a gas through the equation PV = mRT. It is a central concept for analyzing gaseous systems, allowing us to correlate state variables before and after changes in the system, such as during compression in a piston-cylinder setup.

First Law of Thermodynamics for Closed Systems

The first law of thermodynamics states that the change in internal energy of a closed system is equal to the heat added to the system minus the work done by the system. In the context of an adiabatic process, where no heat transfer occurs, this principle shows that the work performed on or by the system is directly responsible for changes in its internal energy and temperature.

Transcript

00:01 Hi, everybody.

00:01 So find the final pressure, final temperature, and piston works.

00:05 So for this, we have mass fraction of oxygen, which is 0 .02, which is 4 eighth in its 50%.

00:19 Mass fraction of argon is 4 .8 equals 50%.

00:27 So now we can do...

00:31 The r mix, which should know how to do this by now, but not.

00:39 That's okay.

00:41 Um, 0 .5 times 48 .28 plus 0 .5.

00:50 This comes from these guys right here, 0 .5 times 38 .68 equals 43 .488 .448 equals 43 .48 eight feet times i be up divided by i bm r okay and we need to get it to b to you so what we're going to do is just divide this by 778 and what we end up getting is 0 .0558 b to you, i, b .m times r, okay? and now we need to find the cp mix, and the c -p mix is the total of the c -i and the cpi.

01:51 So we have 0 .5 times 0 .22 plus 0 .5, 5 times 0 .124.

02:03 Here we get 0 .172, b2, b2, i, b, m, m, r.

02:12 Now we can do the cv, cdi, and it's going to be the exact same way how we did it.

02:21 You see, can mix.

02:22 0 .5 times 0 .158 plus 0 .055 times 0 .07445.

02:35 And this is going to use 0 .11625, b -t -u -i -b -m -r.

02:45 Okay.

02:47 So now after this, we need to find a specific ratio, which is cp over your cd and we get 0 .172.

02:58 Oops, i got the one, divided by 0 .11625 equals 1 .479.

03:07 Okay.

03:09 And so we need to assume the compression process satisfies the law of, yeah, pv, okay, and that's the law.

03:18 And i'm gonna just keep going down so we can solve cool it better p1 over p2 equals v2 over v1 is a key power okay and so now we just plug and chug in here so we got one four set oops one 14 .7 my bad over pressure two over one over two so makes one half and we got one point four seven nine power and we just solve for p2 that's simple algebra so i'm going to do that.

03:53 So we got 40 .977 ibf per inches square...

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