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Chapter 2: Problem 29

Is temperature a state function? Defend your answer.

Short Answer

Expert verified
Yes, temperature is a state function because it depends only on the current state of the system.

Step by step solution

01

Understanding State Functions

A state function is a property of a system that depends only on its current state and not on how it got there. This means that the value of a state function is the same regardless of the process or path taken to reach that state.
02

Analyze Temperature as a System Property

Temperature is a measure of the average kinetic energy of the particles in a substance. It describes the current condition or state of the system in terms of energy distribution.
03

Evaluate Path Dependency

Since temperature reflects a specific condition of the system at a given moment and is independent of the path taken to reach that temperature, it satisfies the criteria for being a state function.

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Key Concepts

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

Temperature as a State Function
Temperature is an instrumental concept in understanding state functions. A state function depends solely on the current state of a system, not the path taken to achieve it. The current temperature of a system quantifies the average kinetic energy of its particles. This makes temperature a reflection of the system鈥檚 current condition rather than its history.
Temperature is not influenced by how a state was achieved. This means the temperature remains consistent regardless of how energy is added or removed from the system. It merely describes a snapshot of the energy within a system.
Fundamentals of Thermodynamics
Thermodynamics is the branch of physics focused on the relationships between heat, work, temperature, and energy. It examines how energy moves and transforms in a system. In thermodynamics, temperature is crucial because it helps determine other thermodynamic quantities such as energy and entropy.
Key principles of thermodynamics include:
  • The Zeroth Law, establishing thermal equilibrium and temperature as a concept.
  • The First Law, which centers on the conservation of energy.
  • The Second Law, addressing the increase of entropy in isolated systems.
  • The Third Law, concerning the behavior of systems as the temperature approaches absolute zero.
Understanding these principles allows us to better comprehend temperature's role as a consistent state function in a thermodynamic system.
Understanding Kinetic Energy and Temperature
Kinetic energy in a system arises from the motion of its particles. The faster the particles move, the greater their kinetic energy. Temperature is a direct measure of this average kinetic energy.
This relationship means that as temperature increases, so does the average kinetic energy of particles. When heat is applied to a system, it increases the particles' speed, subsequently increasing the temperature. Conversely, cooling a system reduces particle speed and lowers temperature.
In essence, temperature acts as an indicator of the energy due to particle motion in a substance, which correlates directly with kinetic energy.
Dissecting Path Dependency
Path dependency describes a situation where the end state of a process depends on the path taken to get there. However, this does not apply to state functions like temperature. For such functions, only the initial and final states matter.
Whether a system is heated slowly or rapidly, as long as it reaches a particular state, its temperature remains unaffected by the journey it took. This independence underscores why temperature is classified as a state function.
In conclusion, temperature's insensitivity to the path taken affirms its role as a reliable metric for understanding a system's energy state, distinct from the specifics of its transition path.

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Most popular questions from this chapter

Under what conditions will \(\Delta U\) be exactly zero for a process whose initial conditions are not the same as its final conditions?

Explain in your own words why work done by the system is defined as the negative of \(p \Delta V\), not positive \(p \Delta V\).

The Dieterici equation of state for one mole of gas is $$ p=R T \frac{e^{-a / V R T}}{\bar{V}-b} $$ where \(a\) and \(b\) are constants determined experimentally. For \(\mathrm{NH}_{3}(g), a=10.91 \mathrm{~atm} \cdot \mathrm{L}^{2}\) and \(b=0.0401 \mathrm{~L}\). Plot the pressure of the gas as the volume of \(1.00 \mathrm{~mol}\) of \(\mathrm{NH}_{3}(g)\) expands from \(22.4 \mathrm{~L}\) to \(50.0 \mathrm{~L}\) at \(273 \mathrm{~K}\), and numerically determine the work done by the gas by measuring the area under the curve.

A 5-mm diameter hailstone has a terminal velocity of \(10.0 \mathrm{~m} / \mathrm{s}\). Assuming its mass is \(6.0 \times 10^{-5} \mathrm{~kg}\) and all of its kinetic energy turns into heat, calculate the temperature change of the hailstone when it hits the ground and stops. The heat capacity of ice is \(2.06 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K}\).

Calculate the work on the system when a piston is compressed by a pressure of 1780 torr from \(3.55 \mathrm{~L}\) to \(1.00 \mathrm{~L}\).
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