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Chapter 18: Problem 5

Are the initial and final equilibrium states of an irreversible process describable by points in a \(p V\) diagram? Explain.

Short Answer

Expert verified
Yes, the initial and final equilibrium states of an irreversible process can be represented by points in a pV diagram. Despite not all the points in the process curve representing genuine physical states of the system during an irreversible process, the initial and final states are still equilibrium states and can be depicted as points on the diagram.

Step by step solution

01

Understand reversible and irreversible processes

In thermodynamics, a reversible process is one that can be reversed by an infinitesimal change in conditions, which means the system and its surroundings can be exactly restored to their initial states. On the other hand, an irreversible process is one which cannot be reversed, which means the system cannot be returned to its original state without changing the surrounding conditions.
02

Apply the concept of reversible and irreversible processes to pV diagrams

A pV diagram for a given process displays transitions between different states of the system. In a reversible process, each intermediate state is one of thermodynamic equilibrium, and every point on the pV diagram is an actual physical state of the system. On the other hand, in an irreversible process, not every intermediate state is an equilibrium state, which means not all points represent genuine physical states of the system.
03

Analyzing initial and final states

However, regardless of whether the process is reversible or irreversible, the initial and final states of the process are equilibrium states. This is because a process by definition involves transition from one equilibrium state to another. Thus, even for an irreversible process, it starts from an initial equilibrium state and concludes at a final equilibrium state.

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Most popular questions from this chapter

An \(8.5-\mathrm{kg}\) rock at \(0^{\circ} \mathrm{C}\) is dropped into a well- insulated vat containing a mixture of ice and water at \(0^{\circ} \mathrm{C}\). When equilibrium is reached, there are \(6.3 \mathrm{g}\) less ice. From what height was the rock dropped?

Prove that the slope of an adiabat at a given point in a \(p V\) diagram is \(\gamma\) times the slope of the isotherm passing through the same point.

One scheme for reducing greenhouse-gas emissions from coalfired power plants calls for capturing carbon dioxide and pumping it into the deep ocean, where the pressure is at least 350 atm. You're called to assess the energy cost of such a scheme for a power plant that produces electrical energy at the rate of 1.0 GW while at the same time emitting \(\mathrm{CO}_{2}\) at the rate of 1100 tonnes/hour. If \(\mathrm{CO}_{2}\) is extracted from the plant's smokestack at \(320 \mathrm{K}\) and 1 atm pressure and then compressed adiabatically to 350 atm, what fraction of the plant's power output would be needed for the compression? Take \(\gamma=1.3\) for \(\mathrm{CO}_{2} .\) (Your answer is a rough estimate because \(\mathrm{CO}_{2}\) doesn't behave like an ideal gas at very high pressures; also, it doesn't include the energy cost of separating the \(\mathrm{CO}_{2}\) from other stack gases or of transporting it to the compression site.)

Find the rate of heat flow into a system whose internal energy is increasing at the rate of \(45 \mathrm{W}\), given that the system is doing work at the rate of \(165 \mathrm{W}\).

The temperature of the water in a jar is raised by violently shaking the jar. Which of the terms \(Q\) and \(W\) in the first law of thermodynamics is involved in this case?
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