1. **Fundamental laws**:

- 1
^{st}, 2^{nd}and 3^{rd}laws of thermodynamics - Mass conservation
- Conservation of linear momentum
- Conservation of angular momentum

**2) Constitutive equations:**

Hopefully describe the macroscopic (i.e. accessible to direct measurement) behaviour of some ** restricted** class of systems in some

An example. Fluid dynamics:

Where

is the ’stress’ tensor;

and are viscosities;

is the ‘thermodynamic pressure’;

is the ‘rate of deformation’ tensor.

Once introduced into the linear momentum balance these equations give the Navier-Stokes equation. Actually thermodynamics, and specifically the 2^{nd} law, imposes * restrictions* on the allowable forms for the constitutive equations as well as for the relationships between them.

**Theory of constitutive equations**: 2^{nd} law does not tell us what the constitutive equations are , but only what they cannot possibly be.

Moreover 2^{nd} law introduces two fundamental distinctions:

**a) REVERSIBLE vs IRREVERSIBLE PHENOMENA**

** b) EQUILIBRIUM vs NON-EQUILIBRIUM CONDITIONS**.

**3) Engineering theory**

Fundamental laws along with constituitve laws are used to solve engineering problems.

**4)Statistical thermodynamics (microscopic theory)**

Molecular-scale models are constructed and constitutive equations can be inferred from such models.

**Body and state**

We introduce here some * primitive concepts* (a primitive concept is something of which we do not give any definition but that we describe by describing its properties).

**BODY**, . It is endowed with a * fixed mass*, , and occupies some

**CONSTITUTIVE EQUATIONS**. Constitutive equations are * assumptions* which may, or may not, adequately describe the behaviour of real bodies. There are several

**1st level**

Some quantity is a physical property of the body considered and, therefore, its value depends only on the* physical condition of existence of the body considered, i.e. on its state*, . Such quantities are called

Hence, a **mapping****exists which maps the state into the value of the constitutive property, L:**

Here and in the following, he subscript ‘t’ indicates that the quantity is referred to the body as a whole.

**2 ^{nd} level**

We now make an assumption about **which quantities determine the state of the body** considered, i.e. to assign a mathematical structure to the state .

There is a restriction: these quantities must, in principle, be measurable by measurements made only on the body itself.

**3 ^{rd} level**

We now assume a * specific functional form for the constitutive mapping*.

Example: the body is a mass of gas

The state of a body as well as the values of all the functions of state may change in time.

We now give the definition of * Process*.

A * Process* is defined as the

*1*. Body, state and constitutive behaviour

*3*. 1st and 2nd principles of thermodynamics. Integral and local forms. The concept of entropy

*4*. State and equilibrium. Part 1

*5*. State and equilibrium. Part 2

*6*. State and equilibrium. Part 3

*7*. State and equilibrium. Part 4

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