An insulated rigid tank is divided into two equal parts by a...

An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains $3 \mathrm{~kg}$ of argon gas at $300 \mathrm{kPa}$ and $70^{\circ} \mathrm{C},$ and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Assuming the surroundings to be at $25^{\circ} \mathrm{C},$ determine the exergy destroyed during this process.

Key Concepts

Exergy

Exergy is the maximum useful work that can be extracted from a system relative to a specified environment (or dead state). It is a measure of the system's potential to cause change when brought into equilibrium with its surroundings and is used to assess the ‘quality’ or usefulness of energy in a process. In exergy analysis, all forms of energy are evaluated not just by their quantity but by their ability to perform work, which inherently depends on the temperature and pressure differences between the system and its environment.

Irreversibility

Irreversibility refers to the inherent losses and generation of entropy during real thermodynamic processes that deviate from the ideal reversible path. It quantifies the degradation in the quality of energy, leading to the loss of available work. In the context of exergy analysis, the irreversibilities in a process, such as mixing or free expansion, account for the exergy destruction, which is the difference between the ideal (reversible) and actual work potentials.

Free Expansion

Free expansion is a process in which a gas expands into a vacuum without doing work on the surroundings and without heat transfer. Although the internal energy remains constant in an ideal free expansion, the process is inherently irreversible. The lack of work interaction means that the energy remains but the ability to do useful work (exergy) is diminished, reflecting the losses due to irreversibility.

Dead State

The dead state is the reference condition where a system is in complete equilibrium with its surroundings, having the same temperature, pressure, and chemical composition. It represents a state of zero exergy, where no further work can be extracted from the system. Exergy calculations often use the dead state as a baseline to evaluate how far a system is from equilibrium and how much useful work can be derived before reaching this state.

Transcript

00:01 Let's say that i have a box which is separated right down the middle.

00:04 And on one side, there's three kilograms of argon gas.

00:11 And on the other side, there is absolutely nothing.

00:13 It is a complete vacuum.

00:15 And this is a closed system.

00:17 There's no heat coming in or out.

00:19 There's only this argon and this vacuum in their own equal volumes of this box.

00:27 So my question is, what is? the entropy generation, and this is directly tied to the way it's phrased elsewhere, which is what is the amount of destroyed exergy.

00:43 These are essentially the same.

00:44 They're trivially related.

00:46 So what is the irreversible energy associated with removing the barrier between these two halves of the box? so that's what we're going to figure out.

00:56 So when we're thinking about the energy balance for this, we know that overall, all the change in energy has to be zero.

01:03 But what's contributing to this energy balance here? there's no heat coming in or out.

01:11 That's definitely true.

01:13 So we're not changing the volume of the system because we have the same volume.

01:19 It's just that they're separated initially.

01:22 So ultimately our total energy balance is only going to consist of internal energy.

01:27 And so in general, what is this equal to? well, it's equal to the mass or the moles, but in this case the mass, times the intensive value of internal energy for each state.

01:43 So, but didn't we say that this is the only thing contributing to our total energy balance? and our total energy balance has to be zero...

Please give Ace some feedback