**First Law of Thermodynamics**

Heat flows from a substance with higher temperature to a substance of lower temperature. The one with the higher temperature loses heat and the one whose temperature is lower gains the heat. That is, the amount of heat lost is always equal to the amount of heat gained – thus, there is conservation of heat energy. If this conservation of heat energy is applied to thermal system, or to systems which involves temperature changes, a new law is formed which states that: *The heat added to a system* is equal to the sum of the change in the internal energy of the system and the external work done by the system.

This law suggests that, when heat is added to a system, the system does any or both of the following situations:

- the heat may be used to increase the system’s internal energy; and
- the heat may be used to do external work (work done by the system).

The first law of thermodynamics may be written mathematically as

\(\mathbf{\Delta Q = \Delta U + W}\),

where \(\Delta Q\) is the heat released or absorbed by the system, \(\Delta U\) is the change in the system’s internal energy, and W is the external work done by the system.

The above equation can also be written in terms of the change in internal energy when heat is added or removed in the system, or work is done by the system, or both. We have

\(\mathbf{\Delta U = \Delta Q - W}.\)

The law differs in different thermodynamic processes. To know this, we must know first what are these different types of processes.

**Thermodynamics and its Processes**

**Thermodynamics **is the study of heat and its transformation into mechanical energy. These terms came from a Greek word which means *movement of heat*.

There are different processes involved in a thermodynamic system. These processes, also called as ** thermodynamic processes**, may be described as any change in the values of the different quantities such as: pressure, volume, temperature, and quantity of a substance. These quantities are also known as state variables.

** State variables** describe the features of the system which is always the same at a certain state of a system. A state means that a system has specified values of pressure, temperature, volume, and amount of a substance.

A process may be reversible or irreversible. ** Reversible** if the process can be done in the reverse direction and

**if the process cannot be made to go in the reverse direction. If series of changes will happen that may result to the return of the system to its initial state, the process is called**

*irreversible***.**

*cycle*The next discussion is about the different thermodynamic processes:

**Adiabatic Process**

In this thermodynamic process, there’s no heat added or removed from the system. The work done on the system increases the internal energy of the system. *Adiabatic wall *is the wall of the system that does not permit the flow of heat through it while *diathermic wall *allows the heat to flow through it. Since \(\Delta Q = 0\), the mathematical expression for this process is: \(\Delta U + W = 0\) or it can be rewritten as \(\Delta U = -W\).

**Isobaric Process**

This process happens when the pressure in the system is constant. The heat added to the system is used to increase the thermal energy and do work. Mathematically, this can be expressed as: \(\Delta Q = \Delta U + P\Delta V\).

**Isothermal Process**

This process involves constant temperature and internal energy. Though temperature in the system remains the same, it still absorbs heat. The energy which is added to the system as heat is used to do work. Given that \(\Delta U = 0\), this process can be represented by the equation: \(\Delta Q = W\).

**Isovolumetric or Isochoric Process**

Isovolumetric process is a constant volume process. The volume of the system does not change, thus, no work is done on the system, \(W = 0\). The heat added to the system is used to increase the internal energy. The first law equation in this process is written as: \(\mathbf{\Delta Q = \Delta U}\).

**Example 1.**

A system absorbs energy of 500 J. How much is the change in the internal energy of the system if the work it does is 450 J?

Given:

\(\Delta Q\) = 500 J

W = 450 J

Solution:

We use the first law of thermodynamics equation to solve for the internal energy of the system. We have \( \mathbf{\Delta U = \Delta Q - W}\). Substitute all the given values,

\(\Delta U = 500\;J – 450\;J = 50\; J.\)

Thus, the change in internal energy of the system is **50 J**,