An insulated vertical piston-cylinder device initially contains 15 kg of water, 13 kg of which

step 1 So we have an insulated vertical piston cylinder device. And we have, so we have, it has water,

An insulated vertical piston-cylinder device initially...

An insulated vertical piston-cylinder device initially contains $15 \mathrm{~kg}$ of water, $13 \mathrm{~kg}$ of which is in the vapor phase. The mass of the piston is such that it maintains a constant pressure of $300 \mathrm{kPa}$ inside the cylinder. Now steam at $2 \mathrm{MPa}$ and $400^{\circ} \mathrm{C}$ is allowed to enter the cylinder from a supply line until all the liquid in the cylinder is vaporized. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine $(a)$ the amount of steam that has entered and $(b)$ the exergy destroyed during this process.

Key Concepts

Thermodynamic Properties of Water and Steam

This concept involves understanding the characteristics of water in its liquid and vapor phases, including properties such as temperature, pressure, quality, and enthalpy. It is crucial for analyzing phase changes in water, especially when steam is added to achieve complete vaporization. The steam tables and phase diagrams provide the necessary thermodynamic properties to quantify mass and energy balances during the process.

Open System (Control Volume) Analysis

In thermodynamics, many processes involve systems where mass enters or leaves, known as open systems or control volumes. This concept is essential for analyzing devices like piston-cylinder assemblies where the introduction or removal of mass affects energy, work, and mass balances. The analysis typically employs the first law of thermodynamics to relate energy exchanges and track the state changes of the working fluid.

Constant Pressure Processes

A constant pressure process is one in which the pressure remains uniform throughout the operation. This is often maintained by external mechanisms, such as a piston with a fixed weight. Understanding constant pressure conditions is vital, as it simplifies the energy analysis and influences the behavior of the fluid during heating or phase change, permitting specific evaluation of enthalpy changes and work interactions.

Exergy Analysis

Exergy analysis assesses the quality or 'useful' portion of energy, quantifying the maximum work obtainable as a system moves towards equilibrium with its surroundings. It provides a measure of how efficiently energy is used, distinguishing reversible and irreversible processes. This concept is fundamental in identifying, quantifying, and minimizing energy losses in thermodynamic processes.

Irreversibility and Exergy Destruction

Irreversibility in a process stems from factors like friction, unrestrained expansions, and thermal gradients, causing a portion of the available energy (exergy) to be lost as waste heat rather than being converted into useful work. Calculating exergy destruction allows engineers to quantify the inefficiencies within a system and to design processes aimed at reducing such losses to improve overall performance.

Transcript

00:01 So we have an insulated vertical piston cylinder device.

00:08 And we have, so we have, it has water, 15 kilograms of water in it at 300 kilopascals.

00:20 The mass of the vapor is 13 kilograms and that of the liquid is 2 kilograms.

00:28 So let's see here.

00:30 Let's draw a little figure here.

00:33 So we have our cylinder, piston cylinder arrangement here.

00:39 And we have some liquid.

00:42 Not a whole lot of liquid.

00:44 Again, this is probably even exaggerated because of the, you know, the densities because we have so much mass of gas.

00:51 But it's going to be not really a whole lot of volume of liquid in here.

00:56 So there's out of the gas.

00:58 And now, let's see here.

01:01 What was going on with this stuff? it maintains a constant pressure.

01:09 Now steam at 2 megapascals and 400 degree c is allowed to enter the cylinder from a supply line.

01:16 Okay, so let's see here.

01:21 We have a supply line here.

01:24 Let's see, draw that down here.

01:29 And we have steam coming in here.

01:36 And it is coming in at 200 megapaths or 2 megapascals and 400.

01:42 100 degrees c, as i said.

01:44 And we do this until the liquid in the cylinder is vaporized.

01:53 So in the end state, all of this stuff is going to be liquid or vapor.

01:59 And again, we'll have a constant pressure.

02:01 And so this steam coming in is going to add energy so that we then vaporize the liquid water that was a little bit of liquid water that was in here.

02:13 So that's what we're doing.

02:15 And we have surrounding conditions here.

02:18 So let's see here.

02:20 Initially, we have the entropy, the entropy, again, because we have the pressure.

02:27 And we have, you know, it is a saturate, oh, it is in the, you know, it's a two phase.

02:38 So we know the temperature.

02:40 And so we know the pressure.

02:42 And then we can figure out, let's see here.

02:44 How did i figure that out, in fact? yeah...