A piston-cylinder device contains 8 kg of refrigerant134 a at 0.7 MPa and 60^∘ C. The refrigera

A piston-cylinder device contains 8 kg of refrigerant134 a...

Key Concepts

Exergy Destruction

Exergy destruction quantifies the loss of useful work potential due to irreversibilities inherent in any real process. These irreversibilities arise from phenomena such as friction, heat transfer across finite temperature differences, and mixing, which all lead to an increase in entropy. In exergy analysis, the destroyed exergy is a measure of the inefficiencies and losses in the process, providing critical insight into how the performance of a system can be improved.

Exergy

Exergy represents the maximum useful work that can be extracted from a system as it reaches equilibrium with its environment. It characterizes the quality or utility of energy by accounting not only for the quantity of energy present but also for how far that energy is from the ambient state. This concept is fundamental to assessing the potential of a system to do work and for comparing different energy forms in terms of their usefulness in practical applications.

Reference Environment

The reference environment, sometimes called the dead state, is a set of properties (pressure, temperature, and composition) representing the surroundings with which the system eventually comes into equilibrium. In exergy analysis, the environmental state serves as the baseline for determining the available work of a system. The concept emphasizes the relative nature of exergy, as the usefulness of energy depends on its difference from these ambient conditions.

Thermodynamic Property Evaluation

Thermodynamic property evaluation involves determining the state properties (such as pressure, temperature, and specific enthalpy and entropy) of a substance, which are essential for calculating energy and exergy. This evaluation is accomplished using empirical data, equations of state, or property tables, and is critical for analyzing processes in closed systems or other devices where energy and work calculations are required.

Closed System Analysis

Closed system analysis pertains to the study of systems where mass remains constant, but energy in the form of work or heat can cross the system boundary. This approach employs the first and second laws of thermodynamics to track energy and entropy changes within the system, allowing for the calculation of performance measures such as exergy and exergy destruction, which are vital for assessing the efficiency of thermodynamic processes.

Transcript

00:01 Let's say that i have a piston cylinder device, which is holding refrigerant r -frigerent r134a, and it is initially at the condition where it has a pressure of 0 .7 megapascals and a temperature of 60 degrees celsius.

00:30 And then we take this and we take the refrigerant inside and we cool it down at constant pressure so that it becomes a liquid.

00:44 And this liquid is going to be at a temperature of 20, 20 degrees celsius.

00:54 So we'll call this t2, call this t1 and this p1.

00:58 And p1 or p2 is going to be equal to p1 since we said we cooled at constant pressure.

01:04 So what we actually want to find here is what is the exergy at each state, state one and two, before and after the cooling, and then what is the amount of exergy destroyed? so these are the things we're going to find.

01:25 So what we need to do first is figure out what x is at each state.

01:29 Okay? so this is going to require looking into the table for the because all of the things that are going to plug into x are state variables so we can find them in the table and you'll remember that x for a given state is going to be equal to the mass of whatever material we're talking about times some coefficient i where the coefficient fee sub i is going to be a equal to the change in the internal energy between the states plus the energy associated with the intensive energy associated with the pressure change.

02:12 So that's going to be the atmospheric pressure times the change in alpha.

02:16 And we're going to subtract off the atmospheric temperature times the change in entropy.

02:22 So that's how we're going to calculate fee for each of these states.

02:26 So what we need now is these, the numbers that are going to going into here, the state values that are going to here, which you'll need to look up in the table.

02:38 And so what i'll do real quick is compile a summary of what you'll find when you go into the table.

02:47 So we're looking for three different sets of values, sets of these parameters.

02:56 One for state one, one for state two, and one for the atmospheric conditions, which are assumed to be an atmospheric temperature of 20 degrees celsius and an atmospheric pressure of 100 kpa.

03:16 So that's what we're assuming our atmospheres like in this problem.

03:23 So we also need to find alpha, internal energy, and entropy values that correspond to that state.

03:30 So this is how i'll do it.

03:32 I'll say atmospheric is going to be state zero.

03:35 I'll say that the initial state is state one and the final state is state two.

03:40 And then we'll fill in this table.

03:42 So these, of course, are going to have units.

03:45 Alpha is going to have units of meters cubed per kilogram.

03:49 Internal energy will have units of kilojoules per kilogram, and entropy will have units of kilojoules per kilogram kelvin.

03:59 Okay, so let's fill this in.

04:02 For the atmospheric state, we're going to get two, three, four.

04:06 I'm going to just do about three significant digits.