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Physics Principles with Applications
Found in: Page 412
Physics Principles with Applications

Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

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Short Answer

Question: (II) A 1.0-L volume of air initially at 3.5 atm of (gauge) pressure is allowed to expand isothermally until the pressure is 1.0 atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating at constant volume. Draw the process on a PV diagram, including numbers and labels for the axes.

The P-V diagram is shown below:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Understanding of isobaric process 

The isobaric process may be described as the thermodynamic process that happens at constant pressure. The volume of the thermodynamic system varies during the isobaric process.

Step 2: Given information 

Given data:

The initial volume of the air is \[{V_{\rm{i}}} = 1.0\;{\rm{L}}\].

The initial gauge pressure of the air is \[{P_{{\rm{i,g}}}} = 3.5\;{\rm{atm}}\].

The final gauge pressure of the air is \[{P_{{\rm{f,g}}}} = 1.0\;{\rm{atm}}\].

Step 3: Evaluation of the final volume of the air                         

The initial absolute pressure of the air can be calculated as:

\[\begin{array}{l}{P_{{\rm{i,a}}}} = {P_{{\rm{i,g}}}} + \left( {1.0\;{\rm{atm}}} \right)\\{P_{{\rm{i,a}}}} = \left( {3.5\;{\rm{atm}}} \right) + \left( {1.0\;{\rm{atm}}} \right)\\{P_{{\rm{i,a}}}} = 4.5\;{\rm{atm}}\end{array}\]

The final absolute pressure of the air can be calculated as:

\[\begin{array}{l}{P_{{\rm{f,a}}}} = {P_{{\rm{f,g}}}} + \left( {1.0\;{\rm{atm}}} \right)\\{P_{{\rm{f,a}}}} = \left( {1.0\;{\rm{atm}}} \right) + \left( {1.0\;{\rm{atm}}} \right)\\{P_{{\rm{f,a}}}} = 2.0\;{\rm{atm}}\end{array}\]

From ideal gas equation, the relation between the pressure and volume is given as:

\[PV = {\rm{constant}}\]

For any two states, the above equation can be written as:

\[\begin{array}{c}{P_{{\rm{i,a}}}}{V_{\rm{i}}} = {P_{{\rm{f,a}}}}{V_{\rm{f}}}\\{V_{\rm{f}}} = \frac{{{P_{{\rm{i,a}}}}{V_{\rm{i}}}}}{{{P_{{\rm{f,a}}}}}}\end{array}\]

Substitute the values in the above equation.

\[\begin{array}{l}{V_{\rm{f}}} = \frac{{\left( {4.5\;{\rm{atm}}} \right)\left( {1.0\;{\rm{L}}} \right)}}{{\left( {2.0\;{\rm{atm}}} \right)}}\\{V_{\rm{f}}} = 2.25\;{\rm{L}}\end{array}\]

Thus, the final volume of the air is \[2.25\;{\rm{L}}\].

Step 4: P-V diagram for the given values

The P-V diagram for the given values can be drawn as:

In the above P-V diagram, curve AB represents the isothermal expansion. In this process pressure changes from \(4.5\;{\rm{atm}}\) to \(2.0\;{\rm{atm}}\) and volume changes from \(1.0\;{\rm{L}}\)to \(2.25\;{\rm{L}}\). The curve BC represents the air compressed at constant absolute pressure of \(2.0\;{\rm{atm}}\). The curve CA represents the air brought back to initial absolute pressure of \(4.5\;{\rm{atm}}\) at constant volume.

Most popular questions for Physics Textbooks

(I) Solar cells (Fig. 15–26) can produce about 40 W of electricity per square meter of surface area if directly facing the Sun. How large an area is required to supply the needs of a house that requires 24 kWh/day? Would this fit on the roof of an average house? (Assume the Sun shines about 9 h/day.).

FIGURE 15-26 Problem 53

(III) A real heat engine working between heat reservoirs at 970 K and 650 K produces 550 J of work per cycle for a heat input of 2500 J.

(a) Compare the efficiency of this real engine to that of an ideal (Carnot) engine.

(b) Calculate the total entropy change of the universe per cycle of the real engine, and

(c) also if the engine is ideal (Carnot).

The oceans contain a tremendous amount of thermal (internal) energy. Why, in general, is it not possible to put this energy to useful work?

Question: In an isobaric compression of an ideal gas,

(a) no heat flows into the gas.

(b) the internal energy of the gas remains constant.

(c) no work is done on the gas.

(d) work is done on the gas.

(e) work is done by the gas.


Question:Think up several processes (other than those already mentioned) that would obey the first law of thermodynamics, but, if they actually occurred, would violate the second law?
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