/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 Water contained in a piston-cyli... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 69

Water contained in a piston-cylinder assembly, initially at \(300^{\circ} \mathrm{F}\), a quality of \(90 \%\), and a volume of \(6 \mathrm{ft}^{3}\), is heated at constant temperature to saturated vapor. If the rate of heat transfer is \(0.3 \mathrm{Btu} / \mathrm{s}\), determine the time, in min, for this process of the water to occur. Kinetic and potential energy effects are negligible.

Short Answer

Expert verified
Solve for mass using specific volumes and then use heat transfer rate and specific enthalpy change to determine the time.

Step by step solution

01

Understand Initial Conditions

The water is initially at \(300^{\text{F}}\) with a quality \( x_1 = 0.90 \). The initial volume \( V_1 \) is 6 ft\(^3\).
02

Find Properties at Initial State

From steam tables, at \( 300^{\text{F}} \), find the saturated liquid and vapor specific volumes, \( v_f \) and \( v_g \). Calculate the initial specific volume \(v_1\) using the formula: \[ v_1 = x_1 v_g + (1 - x_1) v_f \]
03

Calculate Initial Mass

Use the relationship between volume, specific volume, and mass: \[ V_1 = m v_1 \] Solve for mass \( m \): \[ m = \frac{V_1}{v_1} \]
04

Determine Final State

At the final state, the water is a saturated vapor, so quality \( x_2 = 1 \) and specific volume \( v_2 = v_g = 1.0362 \frac{ft^3}{lbm} \).
05

Calculate Heat Required

The heat required to change from initial to final state can be calculated using the formula: \[ Q = m (h_2 - h_1) \] where \( h_2 \) and \( h_1 \) are the specific enthalpies of the final and initial states respectively.
06

Calculate Time Required for Heating

Given the rate of heat transfer \( \.Q = 0.3 \ \text{Btu/s} \), calculate the time required for heating using: \[ time = \frac{Q}{\.Q} \] Convert the time from seconds to minutes

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Piston-Cylinder Assembly
A piston-cylinder assembly is a classic setup in thermodynamics used to understand various processes involving gases and vapors. It consists of a cylinder with a movable piston. The piston can move up or down within the cylinder, allowing the volume inside the cylinder to change.
This assembly is often used to study processes like heating, cooling, compression, and expansion of gases and vapors.
In the given problem, water is contained in a piston-cylinder assembly. The volume changes during the heating process while maintaining constant temperature, demonstrating a typical thermodynamic scenario.
Quality of Steam
The quality of steam, often represented by the symbol **x**, is a measure of the proportion of the mass of steam that is in the vapor phase.
In technical terms, quality is the ratio of the mass of vapor to the total mass of the mixture of liquid and vapor. It ranges from 0 to 1 (or 0% to 100%).
For instance, in the problem, the initial quality is 90%, meaning the water is 90% vapor and 10% liquid at the start. By the end of the process, the quality becomes 100%, indicating that the water is completely in the vapor phase (saturated vapor).
Specific Volume
Specific volume (v) is an important property in thermodynamics, defined as the volume occupied by a unit mass of a substance.
It is usually expressed in units like ft鲁/lbm or m鲁/kg. You can think of it as the 'volume per mass'.
In this problem, the specific volume helps to determine the initial and final volumes of the water mixture. We calculated the initial specific volume using steam tables and the given quality of the initial state.
Specific volume can vary with temperature and pressure, and it is crucial in analyzing and solving thermodynamic problems.
Heat Transfer Rate
The heat transfer rate is the amount of heat energy transferred per unit time.
In the given problem, the rate of heat transfer is provided as 0.3 Btu/s. This tells us how quickly heat is being added to the water in the piston-cylinder assembly.
The heat transfer rate is crucial for determining how long a process will take. In this case, we used it to calculate the time required to transform the water from its initial state to saturated vapor at constant temperature.
The formula used was: \[ time = \frac{Q}{\text{Heat Transfer Rate}} \]
Saturated Vapor
Saturated vapor is a term used to describe a state where a substance is at its boiling point and the liquid and vapor phases coexist in equilibrium.
At this point, any additional heat will cause the liquid to convert into vapor without raising the temperature.
In the problem, the final state of the water is a saturated vapor, meaning it has all converted to the vapor phase at the saturation temperature.
Understanding the concept of saturated vapor is crucial in thermodynamic calculations, especially when dealing with phase changes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is compressed in a piston- cylinder assembly from \(p_{1}=0.7\) bar, \(T_{1}=280 \mathrm{~K}\) to \(p_{2}=11\) bar. The initial volume is \(0.262 \mathrm{~m}^{3}\). The process is described by \(p V^{1.25}=\) constant. Assuming ideal gas behavior and neglecting kinetic and potential energy effects, determine the work and heat transfer for the process, each in kJ, using (a) constant specific heats evaluated at \(300 \mathrm{~K}\), and (b) data from Table A-23. Compare the results and discuss.

Using the tables for water, determine the specified property data at the indicated states. In each case, locate the state on sketches of the \(p-v\) and \(T-v\) diagrams. (a) At \(p=2 \mathrm{MPa}, T=300^{\circ} \mathrm{C}\). Find \(u\), in kJ/kg. (b) At \(p=2.5 \mathrm{MPa}, T=200^{\circ} \mathrm{C}\). Find \(u\), in \(\mathrm{kJ} / \mathrm{kg}\). (c) At \(T=170^{\circ} \mathrm{F}, x=50 \%\). Find \(u\), in Btu/lb. (d) At \(p=100 \mathrm{lbf} / \mathrm{in}^{2}, T=300^{\circ} \mathrm{F}\). Find \(h\), in Btu/lb. (e) At \(p=1.5 \mathrm{MPa}, v=0.2095 \mathrm{~m}^{3} / \mathrm{kg}\). Find \(h\), in \(\mathrm{kJ} / \mathrm{kg}\).

A closed, rigid tank fitted with a paddle wheel contains \(0.1 \mathrm{~kg}\) of air, initially at \(300 \mathrm{~K}, 0.1 \mathrm{MPa}\). The paddle wheel stirs the air for 20 minutes, with the power input varying with time according to \(\dot{W}=-10 t\), where \(\dot{W}\) is in watts and \(t\) is time, in minutes. The final temperature of the air is \(1060 \mathrm{~K}\). Assuming ideal gas behavior and no change in kinetic or potential energy, determine for the air (a) the final pressure, in MPa, (b) the work, in kJ, and (c) the heat transfer, in kJ.

An open container of pure ethanol (ethyl alcohol) liquid is placed on a table in a room. Evaporation occurs until all of the ethanol is gone. Where did the ethanol go? If the ethanol and the room air are taken to be a closed system, can the system be regarded as a pure substance during the process? How many phases are present initially and finally? Explain. Using \(p-v-T\) Data

A piston-cylinder assembly fitted with a slowly rotating paddle wheel contains \(0.13 \mathrm{~kg}\) of air, initially at \(300 \mathrm{~K}\). The air undergoes a constant-pressure process to a final temperature of \(400 \mathrm{~K}\). During the process, energy is gradually transferred to the air by heat transfer in the amount \(12 \mathrm{~kJ}\). Assuming the ideal gas model with \(k=1.4\) and negligible changes in kinetic and potential energy for the air, determine the work done (a) by the paddle wheel on the air and (b) by the air to displace the piston, each in kJ.
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Electricity and Magnetism

Read Explanation

Rotational Dynamics

Read Explanation

Physical Quantities And Units

Read Explanation

Astrophysics

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.