### What is the first law of thermodynamics – definition and equation

Thermodynamics if basically a science of energy. And the definition of energy varies from situation to situation. But in general we can say that energy is the cause of all changes. And this energy situation cannot be explained without thermodynamic laws. And the first law of thermodynamics is the expression which defines the principle of conservation of energy. According to the law of conservation of energy – energy can be transformed from one form to another but cannot be created or destroyed. A term internal energy is often used to explain first law. Read the following article for clear concept about enthalpy, entropy, internal energy, system, boundary and substances.

What is system. boundary ans surroundings in thermodynamics ?
What is substance in thermodynamics?
What is the objective of thermodynamics ? Difference between thermodynamics and heat transfer

## First law of thermodynamics-definitions

The first law of thermodynamics states that the energy of a system is conserved. It states that

Q-W= de ………………. (1)
Where,

Q is the heat added to the system,
W is the work done on the system
And de is the increase of internal energy of the system.

First law of thermodynamics is formulated by stating that, increase in the internal energy (de) is got by the difference of heat supplied to the system (Q) minus the work that has been done by the system into its surrounding.

All quantities in Eq. (1) may be regarded as those referring to unit mass of the system. (In thermodynamics texts it is customary to denote quantities per unit mass by lowercase letters, and those for the entire system by uppercase letters. This will not be done here.)

The internal energy (also called “thermal energy”) is a manifestation of the random molecular motion of the constituents. In fluid flows, the kinetic energy of the macroscopic motion has to be included in the term ‘e’ in Eq. (1) in order that the principle of conservation of energy is satisfied. For developing the relations of classical thermodynamics, however, we shall only include the “thermal energy” in the term e in explaining 1st law of thermodynamics.So in this section we see how energy is conserved in the first law of thermodynamics.

### Difference between heat and internal energy in first law of thermodynamics

It is important to realize the difference between heat and internal energy. Heat and work are forms of energy in transition, which appear at the boundary of the system and are not contained within the matter. In contrast, the internal energy resides within the matter. If two equilibrium states 1 and 2 of a system are known, then Q and W depend on the process or path followed by the system in going from state 1 to state 2.

The change de = e2 – e1, in contrast, does not depend on the path. In short, e is a thermodynamic property and is a function of the thermodynamic state of the system.

Thermodynamic properties are called state functions, in contrast to heat and work, which are path functions.

#### First law of thermodynamics-equation

Frictionless quasi-static processes, carried out at an extremely slow rate so that the system is at all times in equilibrium with the surroundings, are called reversible processes. The most common type of reversible work in fluid flows is by the expansion or contraction of the boundaries of the fluid element. Let v = I/p be the specific volume, that is, the volume per unit mass. Then the work done by the body per unit mass in an infinitesimal reversible process is -pdv, where du is the increase of u.
The first law (Eq. (1)) for a reversible process then becomes
de = dQ - pdv,  (2 )
Provided that Q is also reversible.

#### Equations of State for thermodynamics first law

In simple systems composed of a single component only, the specification of two independent properties completely determines the state or the system. We can write relations such as
p = p (v, T) (thermal equation of state),
e = e (p, T) (caloric equation of stale).  (3)
Such relations are called equations of state. For more complicated systems composed of more than one component, the specification of two properties is not enough to completely determine the state. For example, for sea water containing dissolved salt, the density is a function of the three variables, salinity, temperature, and pressure.

#### Specific Heats explaining the 1st law of thermodynamics

Before we define the specific heats of a substance, we define a thermodynamic property called enthalpy as
H = e + pv ... (4)
This property will be quite useful in our study or compressible fluid flows.
For single-component systems, the specific heats at constant pressure and constant volume are defined as

Cp = (dh/dT)p ... (5)
Cv = (de/dT)v   ... (6)

Above mentioned equations mean that we regard h as a function of p and T, and find the partial derivative of h with respect to T, keeping p constant. Equation (6) has an analogous interpretation. It is important to note that the specific heats as defined are thermodynamic properties, because they are defined in terms of other properties of the system. That is, we can determine Cp and Cv when two other properties of the system (say, p and T) are given. Thus in the understanding of the first law of thermodynamics specific heat certainly have some significance.
For certain processes common in fluid flows, the heat exchange can be related to the specific heats. Consider a reversible process in which the work done is given by p du, so that the first law of thermodynamics has the form of Eq. (2). Dividing by the change of temperature, it follows that the heat transferred per unit mass per unit temperature change in a constant volume process is
(dQ/dT)v = Cv
This shows that CvdT represents the heat transfer per unit mass in a reversible constant volume process, in which the only type of work done is of the pdv type. It is misleading to define C = (dQ/dT) without any restrictions imposed, as the temperature of a constant-volume system can increase without heat transfer, say, by turning a paddle wheel.
In a similar manner, the heat transferred at constant pressure during a reversible process is given by
(dQ/dT)p = Cp
The first law of thermodynamics state the key concepts of internal energy, heat and work done. Many sign conventions are used for expressing the first law of thermodynamics equation. These are sign convention of Clausius, sign convention of IUPAC and quasi-static process.