A mass of 8 kg of helium undergoes a process from an...

A mass of $8 \mathrm{~kg}$ of helium undergoes a process from an initial state of $3 \mathrm{~m}^{3} / \mathrm{kg}$ and $15^{\circ} \mathrm{C}$ to a final state of $0.5 \mathrm{~m}^{3} /$ $\mathrm{kg}$ and $80^{\circ} \mathrm{C}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine the increase in the useful work potential of the helium during this process.

Key Concepts

Thermodynamic State Properties

The analysis of thermodynamic state properties, including temperature, specific volume, and pressure, is fundamental in understanding energy transformations during a process. Changes in these properties influence both the energy and entropy of the system, thereby affecting the quantity of useful work that can be potentially extracted. This analysis is essential for performing an exergy assessment relative to a given reference environment.

Ideal Gas Behavior

When a substance like helium is treated as an ideal gas, its thermodynamic behavior can be described accurately using the ideal gas law and other simplified relationships between pressure, volume, and temperature. This assumption simplifies calculations of state properties such as enthalpy and entropy, which are necessary for determining the work potential of the gas.

Exergy

Exergy is a measure of the maximum useful work that can be extracted from a system as it comes into equilibrium with its surroundings. It accounts for both the energy content and the quality of energy by considering the effects of irreversibility as dictated by the second law of thermodynamics. Evaluating the change in a system's exergy provides a quantification of how its work potential increases or decreases during a process.

Transcript

00:01 Let's say that we have a process which involves taking eight kilograms of helium.

00:08 Um, at an initial temperature of 15.

00:14 Is that 15 i believe, yet 15 um degrees celsius and having an elf of value where alfa has units meters cubed over kilograms.

00:27 So it's sort of like an inverse density.

00:29 This will be three, um, meters cube per kilogram.

00:33 And let's say we take this to a different temperature 80 degrees celsius with a new alfa value, um, of 0.5 meteors cubed her kilogram.

00:48 And let's say that the the conditions of surroundings are 25 degrees celsius and ah, 100 kph pretty close to atmospheric atmospheric conditions.

01:01 So this is what we have and what we want to figure out is the change in exor ji, which you'll you might remember, has the expression that the change in x sergiy is equal to the mass times the change in internal energy, um, plus the effect of changing the alfa value multiplied by three initial pressure or the atmosphere comm pressure conditions that could be changing alfa minus ah, the effect of the entropy generation.

01:38 So that's gonna be the temperature of surroundings times the entry generation.

01:44 So that's the expression that we're going to use to find our total change in x exit g.

01:50 And that's what we want to know.

01:52 So what don't we have here that we can't just look up? well, we can just look up our heat capacity.

01:58 Um, for helium cv kinds of aglionby capacity is going to be 3.11 killer jewels, kill jewels.

02:11 Uh, kelvin.

02:14 Okay, so that's that's a number we can look up we know are constants for the in the ideal gas expression which we're going to use so that that can also be looked up.

02:24 So what we actually need to find is the change in entropy what you can think about, um, finding using gibbs.

02:32 Um, relation, which is tds, is equal to do you plus p d.

02:37 V.

02:38 Which for ds, which is what we want to find we can rearrange to get d you over tea plus p over tee times.

02:47 Dv so this is what we're gonna use to sort of guide us.

02:53 Um and so to do this, this kind of implies we're gonna have to use the ideal gas law.

03:01 Um, soapy over t...

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