Saturated water vapor at 200 kPa is in a constant pressure piston/cylinder device. At this state

Saturated water vapor at 200 kPa is in a constant pressure...

Key Concepts

Superheated Vapor Properties

Heating a saturated vapor at constant pressure causes it to become superheated, meaning its temperature rises above the saturation temperature for that pressure. In the superheated state, the properties (such as specific volume, temperature, and internal energy) must be determined from superheated steam tables or through appropriate approximations (for example, using the ideal gas law as a rough estimate). This concept is crucial for analyzing the final state of a vapor undergoing a phase change process due to heating.

Specific Volume and Volume Doubling

Specific volume is defined as the volume per unit mass of a substance. When the system’s total volume is doubled at constant pressure and mass, the specific volume also doubles. This concept is pivotal because many thermodynamic properties, especially in steam tables or equations of state, are given per unit mass, and scaling the volume directly influences the state of the substance.

Saturated Water Vapor

This concept refers to a state where water vapor is in equilibrium with its condensed phase (liquid) at a given pressure and temperature. In this state, the vapor is at its maximum possible moisture content for that temperature – any further removal of heat or compression would cause condensation. It is a fundamental idea in thermodynamics that helps in identifying the state of a substance before any process such as heating or compression occurs.

Piston?Cylinder Device and Constant Pressure Process

A piston–cylinder device is a common apparatus used to study thermodynamic processes where a movable piston defines the system’s volume. In a constant pressure process, the external pressure remains fixed as the volume changes due to heating or cooling. This setup is instrumental in understanding how changes in volume affect the system’s state variables (such as temperature) when the pressure is held constant.

Transcript

00:01 Okay, so in this problem we have saturated water vapor at the pressure, let's put here the initial pressure, p1 of 200 kilo -pascal.

00:17 Inside a piston, okay? so the piston at this first state have a height, let's call h1, which is 0 .1, middle.

00:32 From the bottom of the cylinder, the piston, okay? and we need to find in this problem, sorry, we need to find in this problem, what is the final height and what is the final temperature if the water, the water reaper, is heated to occupy twice the volume inside the piston.

01:01 So we know that the final volume is two times twice the initial volume.

01:09 So that's our configuration, okay? so how are we going to calculate this? first of all, we need to set up what is the volume, the specific volume, for the first state.

01:24 So in the first state we're going to look in the table b12 and find that the first state we're going to look in the table b12 and find that that v1 needs to be 0 .8857 meters cubic per kilogram.

01:52 Okay? now that we have the volume for the first state we can look to the final state when the volume is twice the volume, the initial volume.

02:04 So in this configuration we're going to look at the table b1.

02:10 3, okay? because we know that the pressure, the final pressure, let's call pressure 2, is going to be the initial pressure.

02:21 We know that the final volume, the volume 2, is 2 times the volume 1, which is just 1 .7714.

02:39 So we just need to multiply this density here.

02:45 Okay, knowing the state, the final state, we can finally calculate what the problem wants.

02:52 And the first thing we need to calculate is the final height.

02:56 The height has a relation with the volume.

03:03 So we know that h2 is going to be h1.

03:10 V2 divided by v1, sorry this is a 1.

03:14 And that's basically two times, 2 times h1...

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