# The First Law of Thermodynamics Revision Notes

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13.5The First Law of Thermodynamics

In these revision notes for The First Law of Thermodynamics, we cover the following key points:

• What is a system in thermodynamics? How does it differ from surroundings?
• What kind of systems are there in thermodynamics?
• What is the meaning of the state of a system?
• What are thermal processes?
• What is the meaning of internal energy? Where does it depend on?
• How can we give energy to a thermodynamic system?
• What is the meaning of work in thermodynamics?
• What does the First Law of Thermodynamics say?
• What are some Special Cases of the First Law of Thermodynamics?

## The First Law of Thermodynamics Revision Notes

In thermodynamics, a system is a definite group of objects or substances that we choose to study. We must specify well what objects and properties are part of a given system and what are not. Everything out of the system's boundary belongs to the surroundings of the system. The choice of a system in thermodynamics is an arbitrary action. However, a clear definition of the system boundary is very important.

1. Closed systems, in which there is no matter transfer between the system and its surroundings.
2. Isolated systems, in which neither matter nor energy is transferred between the system and its surroundings.
3. Open systems, in which both matter and energy transfer can occur between the system and the surroundings.

Each system has its own set of properties, which describe the state of the given system. To describe a certain state of a system, we must choose the properties that describe in full the exact condition of it. There are only three variables used to describe a thermodynamic system. They are pressure, volume and temperature. Specified values of P, V and T give the state of a gas.

State variables are those variables that always have the same value when the system is in a given state. Pressure, volume and temperature are state variables for a gas. Internal energy is also a state variable.

Equilibrium state for a gas implies that temperature (and therefore pressure and density) of the gas sample has the same value in all parts of its volume. When a gas sample is in equilibrium, its microscopic parameters such as the individual speeds of molecules will change over time. On the other hand, macroscopic parameters involving average effects of many molecules such as pressure, volume and temperature stay constant with time. When a gas sample is in equilibrium, it has definite values of pressure and temperature. In other words, pressure or temperature of a gas have well defined values only when the gas sample is in an equilibrium state.

Any change from one thermodynamic state to another is called a thermal process. Slow processes are much easier to analyze than fast processes.

The total average kinetic energy of gas molecules is equal to the internal energy U, and also it is proportional to the temperature T. Thus,

U = constant × N × T

This expression means internal energy of a thermodynamic system is a function of temperature. In other words, we cannot change the internal energy of a gas without changing its temperature.

There are three possible cases in this regard:

∆U > 0 ⟺ ∆T > 0
∆U = 0 ⟺ ∆T = 0
∆U < 0 ⟺ ∆T < 0

This is not always true for solids and liquids as during the phase change, their internal energy changes without any change in temperature.

There are two possible ways to provide energy to a thermodynamic system.

1. By providing heat to the system. For example, we can use a heat source to transfer energy to a gas by heating it.
2. By doing work on the system. For example, if we push down the piston of a cylinder, we do work on the gas and as a result, its internal energy increases even if no heat is supplied to the gas.

Since internal energy is proportional to the temperature, both the abovementioned ways of energy transfer bring an increase in gas temperature.

By definition, mechanical work W, is defined as an energy transfer to or from a system, not resulting from temperature difference.

• when the gas is expanding, Wdone by the gas is positive and Wdone on the gas is negative
• when the gas is contracting, Wdone by the gas is negative and Wdone on the gas is positive

### The First Law of Thermodynamics states:

The increase in internal energy of a thermodynamic system is equal to the heat added to the system plus the work done on the system.

In symbols, we have:

∆U = Q + Won the system

This equation represents the law of energy conservation in its simplest form. In many cases, we are interested on the work done by the system. Hence, we can write:

∆U = Q - Wby the system

or

Q = ∆U + Wby the system

The last formula is interpreted as:

"The heat supplied to a thermodynamic system, partly goes for the increase in the internal energy of the system and partly for work done by the system on the surroundings."

Thus,

ΔU is positive if the internal energy increases. (Temperature increases).

ΔU is negative if the internal energy decreases. (Temperature decreases).

Q is positive, if heat is added to the system.

Q is negative, if heat flows out of the system.

Wby gas is positive, if work is done by the gas to lift the piston.

Wby gas is negative, if work is done on the gas, decreasing thus the volume.

There are four special cases in the application of the First Law of Thermodynamics.

I. Adiabatic process. This process occurs very rapidly or it occurs in such a well-insulated system, so that no heat is transferred to or by the system. This means Q = 0 and the mathematical expression of the First Law of Thermodynamics becomes

∆U = -Wby the system

II. Constant volume processes. If the volume of a thermodynamic system remains constant for any reason, there is no work done on or by the system (W = 0).

Mathematically, we can write:

Q = ∆U

III. Cyclical processes. In some thermodynamic processes, the system parameters return to their original values after experiencing a number of changes in heat and work. We say the system is restored to its initial state. These are known as cyclical processes. During such processes, no change in the internal energy does occur (ΔU = 0).

Mathematically, we can write

Q = Wby the system

IV. Free expansion processes. In such processes, there is no change in the internal energy of the system and also there is no heat supplied to or removed by the system. Therefore, we have Q = 0, ΔU = 0 and W = 0.

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