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5.1.4.a - (a) Work

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Introduction to Adiabatic Systems

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Teacher
Teacher

Today we'll explore adiabatic systems, where there is no heat exchange with the surroundings. Can anyone tell me what an adiabatic wall is?

Student 1
Student 1

Isn't it the wall that keeps heat from leaving the system?

Teacher
Teacher

Exactly! An adiabatic wall prevents heat transfer. This processing is crucial for understanding changes in internal energy when we perform work.

Student 2
Student 2

What kind of work are we talking about?

Teacher
Teacher

Great question! We'll look at both mechanical and electrical work tonight. Remember, in an adiabatic process, the internal energy changes due to work performed on the system.

Student 3
Student 3

Right! So we can't just add heat to make a change?

Teacher
Teacher

Correct, no heat exchange means only work can alter the internal energy.

Teacher
Teacher

Let's summarize: adiabatic systems don't exchange heat and only work can modify their internal energy.

Work and Internal Energy

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Teacher
Teacher

Now let’s discuss how work affects internal energy in our adiabatic system. What happens to internal energy when we do work on it?

Student 4
Student 4

It should increase, right?

Teacher
Teacher

Exactly! When we do work on the system, such as churning water, the internal energy increases, which corresponds to a rise in temperature.

Student 1
Student 1

And it doesn't matter whether it's mechanical or electrical work?

Teacher
Teacher

Correct! Joule discovered that no matter how you produce the work, the outcome is the same—meaning temperature change is consistent regardless of the work type.

Student 2
Student 2

So, is internal energy a state function?

Teacher
Teacher

Exactly. Internal energy is a state function! It depends on the state of the system and not how we got there.

Teacher
Teacher

Recall: ∆U = U2 – U1 = wad. This shows that changes in internal energy directly relate to the work done.

Understanding State Functions

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Teacher
Teacher

Now that we understand internal energy, can anyone name some other state functions?

Student 3
Student 3

Temperature and volume!

Teacher
Teacher

Exactly! Temperature and volume are also state functions since changes depend only on the current state, not the path taken.

Student 4
Student 4

So if I heat water from 25°C to 35°C, the way I do it doesn’t matter?

Teacher
Teacher

That's correct! It could be fast heating or slow cooling; the result will just be the temperature change from 25 to 35°C.

Student 2
Student 2

Does this apply to all thermodynamic processes?

Teacher
Teacher

Yes! All state functions exhibit this property, making them very useful in thermodynamics.

Teacher
Teacher

To recap, state functions are properties determined by the current state, independent of how that state was reached.

Sign Conventions in Thermodynamics

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Teacher
Teacher

Let’s finalize our session by discussing the sign conventions for work and internal energy. What happens when work is done on the system?

Student 1
Student 1

The internal energy increases, right?

Teacher
Teacher

You got it! Hence, wad is positive in this case. Conversely, if the system does work, wad is negative.

Student 3
Student 3

And ICRAP stands for Internal Change Requires Additional Performance?

Teacher
Teacher

Almost! It’s not so catchy! The key is remembering IUPAC's recommendation for these sign conventions.

Student 2
Student 2

Are there exceptions?

Teacher
Teacher

Typically, no exceptions to these conventions in thermodynamics exist, but they might differ slightly between physics and chemistry contexts.

Teacher
Teacher

To conclude, work done on the system increases internal energy while work done by the system decreases it.

Introduction & Overview

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Quick Overview

This section explores the concept of work done on a system and its impact on internal energy in adiabatic processes.

Standard

The section discusses how work affects the internal energy of a system in an adiabatic process, exemplifying mechanical and electrical work. It highlights the significance of internal energy as a state function and introduces Joule's observations on work and temperature changes.

Detailed

In the adiabatic process defined in this section, a system, such as a thermally insulated beaker containing water, is analyzed for changes in internal energy without heat exchange with the environment. By performing work on this system in two ways—mechanical work (e.g., churning water) and electrical work (using an immersion rod)—it demonstrates that the internal energy change (∆U) is directly correlated to the work done (wad). J. P. Joule's experiments established that the amount of work done on the system results in the same temperature change regardless of the method, reinforcing the definition of internal energy as a state function. Moreover, the section explains the sign conventions in thermodynamics and compares other familiar state functions like volume (V), pressure (p), and temperature (T), noting how changes in these quantities are independent of the process undertaken to achieve them.

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Audio Book

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Understanding Adiabatic Systems

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Let us first examine a change in internal energy by doing work. We take a system containing some quantity of water in a thermos flask or in an insulated beaker. This would not allow exchange of heat between the system and surroundings through its boundary and we call this type of system as adiabatic. The manner in which the state of such a system may be changed will be called adiabatic process. Adiabatic process is a process in which there is no transfer of heat between the system and surroundings. Here, the wall separating the system and the surroundings is called the adiabatic wall.

Detailed Explanation

An adiabatic system is one that does not allow heat exchange with its environment. This means that any changes in the system’s energy are due only to work done on the system or by the system, not due to heat transfer. This is important in thermodynamics because it helps isolate the effects of work on a system's internal energy.

Examples & Analogies

Imagine a thermos containing hot coffee. It keeps the coffee hot without letting heat escape, just like an adiabatic system. Changes in the coffee's state (like cooling down) can happen only if you remove the coffee (work done on the system) or add some ice (work done by the system).

Change in Internal Energy through Work

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Let us bring the change in the internal energy of the system by doing some work on it. Let us call the initial state of the system as state A and its temperature as TA. Let the internal energy of the system in state A be called UA. We can change the state of the system in two different ways.

Detailed Explanation

We can alter the internal energy of the system by performing work, starting from an initial state (A) with a defined temperature and internal energy. There are two methods to do this, each resulting in a change in temperature and internal energy.

Examples & Analogies

Think of a bicycle pump: by pushing down the handle (doing work), you compress the air inside. This compression is analogous to changing the internal energy, increasing temperature as a result of work done.

Two Methods of Work Done

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One way: We do some mechanical work, say 1 kJ, by rotating a set of small paddles and thereby churning water. Let the new state be called B state and its temperature, as TB. It is found that TB > TA and the change in temperature, ∆T = TB–TA. Let the internal energy of the system in state B be UB and the change in internal energy, ∆U = UB– UA. Second way: We now do an equal amount (i.e., 1kJ) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is same as in the earlier case, say, TB – TA.

Detailed Explanation

There are two ways to do work on the system: mechanical work (churning water with paddles) and electrical work (using an immersion rod). Regardless of the method used, both lead to the same increase in temperature and internal energy of the system, demonstrating that the effect of work done on the system is path-independent.

Examples & Analogies

Imagine two ways to heat water: stirring water in a pot with a spoon (mechanical work) versus placing an electric kettle in water (electrical work). Both methods achieve the same result: hot water, showing that the source of energy does not matter.

The Concept of Internal Energy

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In fact, the experiments in the above manner were done by J. P. Joule between 1840–50 and he was able to show that a given amount of work done on the system, no matter how it was done (irrespective of path) produced the same change of state, as measured by the change in the temperature of the system. So, it seems appropriate to define a quantity, the internal energy U, whose value is characteristic of the state of a system, whereby the adiabatic work, wad required to bring about a change of state is equal to the difference between the value of U in one state and that in another state, ∆U i.e., ∆U = U2 – U1 = wad.

Detailed Explanation

J. P. Joule's experiments revealed that the change in internal energy of a system can be consistently described using the concept of internal energy, a property that characterizes the state of a system. The work done on the system is directly related to the difference in internal energy between two states, reinforcing the consistency of energy conservation in thermodynamics.

Examples & Analogies

Consider a comprehensive fitness tracker that records your physical changes regardless of the workout type (running, weight lifting, yoga). Similar to the tracker, internal energy provides a clear measure of the system's state, which remains consistent regardless of the method used to achieve it.

Understanding State Functions

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Therefore, internal energy, U, of the system is a state function. By conventions of IUPAC in chemical thermodynamics. The positive sign expresses that wad is positive when work is done on the system and the internal energy of system increases. Similarly, if the work is done by the system, wad will be negative because internal energy of the system decreases.

Detailed Explanation

Internal energy is classified as a state function, meaning it depends only on the current state of the system and not on the way the state was reached. This is true for other properties like pressure (p), volume (V), and temperature (T). Work done on or by the system is denoted positively or negatively based on whether the internal energy increases or decreases.

Examples & Analogies

Imagine filling a balloon with air: adding air (work done on the system) adds energy, while letting air out (work done by the system) decreases energy. Both scenarios illustrate that the energy of the system (the balloon's internal energy) is decided by its current state, not by how it got there.

Examples of Other State Functions

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Can you name some other familiar state functions? Some of other familiar state functions are V, p, and T. For example, if we bring a change in temperature of the system from 25°C to 35°C, the change in temperature is 35°C–25°C = +10°C, whether we go straight up to 35°C or we cool the system for a few degrees, then take the system to the final temperature. Thus, T is a state function and the change in temperature is independent of the route taken. Volume of water in a pond, for example, is a state function, because change in volume of its water is independent of the route by which water is filled in the pond, either by rain or by tubewell or by both.

Detailed Explanation

Other state functions include volume (V), pressure (p), and temperature (T). These parameters define the condition of a system, and any changes are consistent regardless of how those changes are achieved. This illustrates the inherent independence of state functions from the path taken to reach a certain state.

Examples & Analogies

Picture a road trip: whether you take the highway, a scenic route, or detours, you’ll still end up going the same distance (change in volume) by the end. Your destination (final state) is unaffected by the way you traveled (the path taken). This demonstrates how state functions work.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Adiabatic Process: A process where no heat is transferred between the system and surroundings.

  • Joule's Law: Work done on a system results in the same energy change regardless of the method used.

  • Internal Energy as a State Function: Internal energy depends on the system's state, not the path taken to achieve it.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • When you use a bicycle pump, compressing the air increases its temperature, demonstrating mechanical work affecting internal energy.

  • Using an immersion heater in water heats it up, showing how electrical work also leads to changes in internal energy.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • In adiabatic ways, heat can't sway; work will change the data displayed.

📖 Fascinating Stories

  • Imagine a sealed thermos filled with hot coffee. No heat escapes while you stir it. Regardless of whether you stir with a spoon or mix in sugar, the coffee stays hot, changing temperature only through your work. That's the heart of adiabatic!

🧠 Other Memory Gems

  • Remember 'A WET' - Adiabatic, Work, Energy, Temperature; all closely tied in thermodynamics!

🎯 Super Acronyms

S.U.C.C.E.S.S. - S for State function, U for Internal Energy, C for Changes, C for Work Done, E for Energy transfer, S for System involved.

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Adiabatic Process

    Definition:

    A thermodynamic process in which there is no heat transfer between the system and its surroundings.

  • Term: Internal Energy (U)

    Definition:

    The total energy contained within a system, which is a state function dependent only on the system's state.

  • Term: State Function

    Definition:

    A property of a system that depends only on its current state, not on how it reached that state.

  • Term: Work Done (wad)

    Definition:

    The energy transferred to or from the system by mechanical or electrical means.