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Chapter 1: Problem 6

Can the value of an intensive property such as pressure or temperature be uniform with position throughout a system? Be constant with time? Both?

Short Answer

Expert verified
Yes, an intensive property like pressure or temperature can be uniform with position, constant with time, or both.

Step by step solution

01

Understand Intensive Properties

Intensive properties, unlike extensive properties, do not depend on the amount of matter present. Examples include pressure, temperature, and density.
02

Uniform with Position

An intensive property can be uniform with position if it does not change from one location to another within the system. For instance, pressure can be uniform throughout a closed container of gas under equilibrium.
03

Constant with Time

An intensive property can be constant with time if it does not vary as time progresses. For example, the temperature of a well-insulated object left in a thermally stable environment can remain constant over time.
04

Both Uniform with Position and Constant with Time

An intensive property can be both uniform with position and constant with time. For instance, in an isolated system in thermal equilibrium, the temperature can be the same at all points and remain steady over time.

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Key Concepts

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

Pressure Uniformity
Pressure is an intensive property, meaning it is independent of the amount of substance present in a system.
For pressure to be uniform throughout a system, it needs to be the same at every point within that system.
  • In a closed container filled with gas, if the system is in equilibrium, the pressure is uniformly distributed.
  • This means that no matter where you measure the pressure, the value will be the same.
When pressure is uniform within a system, it implies that the system is in a state of equilibrium with no gradients that might cause fluid flow or other dynamic behavior.
This is crucial for understanding and applying many thermodynamic principles and calculations.
Temperature Stability
Temperature stability refers to the consistency of temperature over time within a system.
  • For instance, a well-insulated container can maintain its temperature over a prolonged period, assuming no heat is added or removed.
  • Such a system is considered thermally stable.
The concept is crucial when studying energy transfer and phase changes because many processes assume a constant temperature to simplify calculations and predictions.
By ensuring the system is thermally stable, we can better predict outcomes of various thermodynamic processes.
Thermal Equilibrium
Thermal equilibrium is a state where there is no net heat flow within the system or between the system and its surroundings.
  • In this state, all components of the system have the same temperature.
  • This uniform temperature is constant over time if the system is isolated.
When a system reaches thermal equilibrium, it implies perfect stability in terms of temperature distribution.
A system in thermal equilibrium is crucial for applying thermodynamic laws effectively, enabling accurate predictions and calculations in energy exchanges and transformations.

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Most popular questions from this chapter

A \(2.2 \mathrm{~m}^{3}\) tank contains water vapor at \(10340 \mathrm{kPa}\) and \(633 \mathrm{~K}\). If the pressure, \(p\), specific volume, \(v\), and temperature, \(T\), of water vapor are related by the expression $$ p=[(7183.04) T /(v-0.0169)]-\left(25.02 \times 10^{3}\right) / v^{2} $$ where \(v\) is in \(\mathrm{m}^{3} / \mathrm{kg}, T\) is in \(\mathrm{K}\), and \(p\) is in \(\mathrm{kPa}\), determine the mass of water in the tank. Also, plot pressure versus specific volume for the isotherms \(T=667,778\), and \(889 \mathrm{~K}\).

Based on the macroscopic view, a quantity of air at \(100 \mathrm{kPa}\), \(20^{\circ} \mathrm{C}\) is in equilibrium. Yet the atoms and molecules of the air are in constant motion. How do you reconcile this apparent contradiction?

An open storage tank is placed at the top of a building. The tank contains water up to a depth of \(1.5 \mathrm{~m}\). Calculate the pressure at the bottom of the tank. It is given that atmospheric pressure is \(101.3 \mathrm{kPa}\) and density of water is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\)

Consider a leaf blower driven by a gasoline engine as the system. Would it be best analyzed as a closed system or a control volume? Are there any environmental impacts associated with such a leaf blower? Repeat if it were an electricallydriven leaf blower.

Owing to strong local winds and large elevation differences on the Hawaiian island of Maui, it may be a suitable place to combine a wind farm with pumped hydro energy storage. At times when the wind turbines produce excess power, water is pumped to reservoirs at higher elevations. The water is released during periods of high electric demand through hydraulic turbines to produce electricity. Develop a proposal to meet \(30 \%\) of the island's power needs by the year 2020 using this renewable energy concept. In your report, list advantages and disadvantages of the proposed system. Include at least three references.
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