A gas undergoes two processes. In the first, the volume remains constant at 0.2000.2000.200 m3 and the pressure increases from 2.00×1052.00\$$times10^52.00×105 Pa to 5.00×1055.00$$\$$times10^55.00×105 Pa. $$The second process is a compression to a volume of 0.1200.1200.120 m3 at a constant pressure of 5.00×1055.00\$$times10^55.00×105 Pa. In a $$pVpV-diagram, show both processes.

Ch 19: The First Law of Thermodynamics

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 19: The First Law of Thermodynamics

문제 6a

19장, 문제 6a

A gas undergoes two processes. In the first, the volume remains constant at $0.200$ m³ and the pressure increases from $2.00$\times$10^5$ Pa to $5.00$\times$10^5$ Pa. The second process is a compression to a volume of $0.120$ m³ at a constant pressure of $5.00$\times$10^5$ Pa. In a $p V$ -diagram, show both processes.

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Start by understanding the pV-diagram, which is a graphical representation of the pressure (p) versus volume (V) for a given process. In this problem, we have two distinct processes to represent.

For the first process, the volume remains constant at 0.200 m^3 while the pressure increases from 2.00 * 10^5 Pa to 5.00 * 10^5 Pa. On a pV-diagram, this is represented as a vertical line because the volume does not change, only the pressure does.

For the second process, the gas is compressed to a volume of 0.120 m^3 at a constant pressure of 5.00 * 10^5 Pa. On a pV-diagram, this is represented as a horizontal line because the pressure remains constant while the volume decreases.

To plot these processes on the pV-diagram, start by marking the initial point of the first process at (0.200 m^3, 2.00 * 10^5 Pa). Draw a vertical line up to the point (0.200 m^3, 5.00 * 10^5 Pa) to represent the first process.

Next, from the endpoint of the first process, draw a horizontal line to the point (0.120 m^3, 5.00 * 10^5 Pa) to represent the second process. This completes the representation of both processes on the pV-diagram.

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주요 개념

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Pressure-Volume (pV) Diagram

A pV diagram is a graphical representation of the changes in pressure and volume of a gas during thermodynamic processes. It helps visualize how these properties interact, with pressure on the y-axis and volume on the x-axis. In this question, the diagram will show a vertical line for the constant volume process and a horizontal line for the constant pressure process.

Isovolumetric Process

An isovolumetric process, also known as an isochoric process, occurs when the volume of a system remains constant. During this process, any change in pressure is due to changes in temperature or the amount of gas. In the given question, the first process is isovolumetric, where the pressure increases while the volume remains at 0.200 m^3.

Isobaric Process

An isobaric process is a thermodynamic process in which the pressure remains constant while the volume changes. This type of process is represented by a horizontal line on a pV diagram. In the question, the second process is isobaric, where the gas is compressed to a volume of 0.120 m^3 while maintaining a constant pressure of 5.00 * 10^5 Pa.

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교과서 질문

A gas undergoes two processes. In the first, the volume remains constant at $0.200$ m³ and the pressure increases from $2.00 \times 10^{5}$ Pa to $5.00 \times 10^{5}$ Pa. The second process is a compression to a volume of $0.120$ m³ at a constant pressure of $5.00 \times 10^{5}$ Pa. Find the total work done by the gas during both processes.

The graph in Fig. E $19.4$ shows a $pV$ -diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) The process illustrated here is somewhat different from those we have been studying, because the pressure change is due to changes in the amount of gas in the lung, not to temperature changes. (Think of your own breathing. Your lungs do not expand because they've gotten hot.) If the temperature of the air in the lung remains a reasonable $20$ °C, what is the maximum number of moles in this person's lung during a breath?

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교과서 질문

Figure E $19.8$ shows a $p V$ -diagram for an ideal gas in which its absolute temperature at $b$ is one-fourth of its absolute temperature at $a$ . Did heat enter or leave the gas from $a$ to $b$ ? How do you know?

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교과서 질문

In Fig. $19.7$ a, consider the closed loop $1 right arrow 3 right arrow 2 right arrow 4 right arrow 1$ . This is a cyclic process in which the initial and final states are the same. Find the total work done by the system in this cyclic process, and show that it is equal to the area enclosed by the loop.

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is $27.0$ °C and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done $2.40 times 10 cubed$ J of work.

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