College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Learning Goal:**
To understand the meaning and the basic applications of \( pV \) diagrams for an ideal gas.
As you know, the parameters of an ideal gas are described by the equation
\[ pV = nRT, \]
where \( p \) is the pressure of the gas, \( V \) is the volume of the gas, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the absolute temperature of the gas. It follows that, for a portion of an ideal gas,
\[ \frac{pV}{T} = \text{constant}. \]
One can see that, if the amount of gas remains constant, it is impossible to change just one parameter of the gas: At least one more parameter would also change. For instance, if the pressure of the gas is changed, we can be sure that either the volume or the temperature of the gas (or, maybe, both!) would also change.
To explore these changes, it is often convenient to draw a graph showing one parameter as a function of the other. Although there are many choices of axes, the most common one is a plot of pressure as a function of volume: a \( pV \) diagram.
In this problem, you will be asked a series of questions related to different processes shown on a \( pV \) diagram (Figure 1). They will help you ...
**Figure 1:**
The figure is a \( pV \) diagram with the x-axis labeled as volume (\( V \)) and the y-axis as pressure (\( p \)). The graph shows a closed loop with points marked at \( V_0, 2V_0, \) and \( 3V_0 \) along the x-axis and at \( p_0, 2p_0, \) and \( 3p_0 \) along the y-axis. The graph includes a series of line segments forming a triangle, representing different thermodynamic processes.
**Part A:**
Calculate the work \( W \) done by the gas during process \( 1 \rightarrow 2 \).
Express your answer in terms of \( p_0 \) and \( V_0 \).
\[ W = 6p_0V_0 \]
Correct
**Part B:**
Calculate the work \( W \) done by the gas during process \( 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d048756-cb3c-4a66-972f-914bd1ae9336%2F4cfc0f3a-ec16-4973-b856-cde233990b3d%2Ff5zkw6r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Learning Goal:**
To understand the meaning and the basic applications of \( pV \) diagrams for an ideal gas.
As you know, the parameters of an ideal gas are described by the equation
\[ pV = nRT, \]
where \( p \) is the pressure of the gas, \( V \) is the volume of the gas, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the absolute temperature of the gas. It follows that, for a portion of an ideal gas,
\[ \frac{pV}{T} = \text{constant}. \]
One can see that, if the amount of gas remains constant, it is impossible to change just one parameter of the gas: At least one more parameter would also change. For instance, if the pressure of the gas is changed, we can be sure that either the volume or the temperature of the gas (or, maybe, both!) would also change.
To explore these changes, it is often convenient to draw a graph showing one parameter as a function of the other. Although there are many choices of axes, the most common one is a plot of pressure as a function of volume: a \( pV \) diagram.
In this problem, you will be asked a series of questions related to different processes shown on a \( pV \) diagram (Figure 1). They will help you ...
**Figure 1:**
The figure is a \( pV \) diagram with the x-axis labeled as volume (\( V \)) and the y-axis as pressure (\( p \)). The graph shows a closed loop with points marked at \( V_0, 2V_0, \) and \( 3V_0 \) along the x-axis and at \( p_0, 2p_0, \) and \( 3p_0 \) along the y-axis. The graph includes a series of line segments forming a triangle, representing different thermodynamic processes.
**Part A:**
Calculate the work \( W \) done by the gas during process \( 1 \rightarrow 2 \).
Express your answer in terms of \( p_0 \) and \( V_0 \).
\[ W = 6p_0V_0 \]
Correct
**Part B:**
Calculate the work \( W \) done by the gas during process \( 2
Expert Solution
Step 1
Given
At point 1 :: pressure ,3po
Volume , Vo
At point 2 :: pressure ,3po
Volume , 3Vo
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