5.1.4.a. (a) Work

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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