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Chemical Thermodynamics 2013/2014

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ChemicalThermodynamics2013/2014

3rd Lecture: Work, Heat and the First Law of Thermodynamics

Valentim M B Nunes, UD de Engenharia

Introduction

As we saw before, thermodynamics it’s a science that studies energy transformations but, as we will see, thermodynamics describes macroscopic properties of equilibrium systems.

Although everybody as the feeling of knowing what is energy, it is very difficult to give a precise definition. For our purposes Energy can be defined as the ability to cause changes or realize Work.

One of the fundamental laws of nature is the law of conservation of energy. Energy in a system may take on various forms (e.g. kinetic, potential, heat, light) but energy may neither be created nor destroyed.

Some basic concepts

Thermodynamic System – it’s a part of the Universe that is being studied.

Exterior or Surroundings of the system – all the rest of the Universe

Boundary of the system – its what divides the system from the rest of the universe.

Surroundings

System

Universe = System + Surroundings

Types of systems

Isolated System – An isolated system is that in which no transfer of mass & energy takes place across the boundaries of system

Closed System - A closed system in which no transfer of mass takes place across the boundaries of system but energy transfer is possible

Open System - An open system is one in which both mass & energy transfer takes place across the boundaries

Describing Systems

To describe a given system we need to indicate the components of the system, their physical state (gas, liquid, solid, mixtures) and the state properties, like pressure, p, volume, V, number of moles, n, mass, m, and temperature, T.

Properties of a system

When one system suffers a transformation it goes from an initial state to a final state. The properties of the system that are univocally determined by the sate of the system are state functions (or state variables or state properties).

These properties may be either intensive or extensive. Extensive properties depends on the size or extension of the system, like the volume, V. Intensive properties are independent of the size of the system, like temperature or pressure.

If we divide an extensive property by the number of moles we obtain an intensive property, like the molar volume:

State of a System at Equilibrium

The state of equilibrium is defined by the macroscopic properties and is independent of the history of the system.

Cooling

Heating

Change of state

A process or transformation is a change in the state of the system over time, starting with a definite initial state and ending with a definite final state.

The process is defined by a path, which is the continuous sequence of consecutive states through which the system passes, including the

initial state, the intermediate states, and the final state

There are many types of processes to change the state of a system - at constant volume (isochoric), at constant pressure (isobaric), at constant temperature (isotherm) and so one..

Infinitesimal Changes

An infinitesimal change of the state function X is written dX. The mathematical operation of summing an infinite number of infinitesimal changes is integration, and the sum is an integral. The sum of the infinitesimal changes of X along a path is a definite integral equal to X:

If dX obeys this relation—that is, if its integral for given limits has the same value regardless of the path—it is called an exact differential. The differential of a state function is always an exact differential

Cycles

A cyclic process is a process in which the state of the system changes and then returns to the initial state. In this case the integral of dX is written with a cyclic integral.

Since a state function X has the same initial and final values in a cyclic process, X2 is equal to X1 and the cyclic integral of dX is zero:

Internal energy

The total energy of a system is the Internal Energy, U. The internal energy is a state function. If a system as an initial energy Ui and after a transformation as a n energy Uf then the variation of internal energy, U is:

The internal energy is an extensive property, that is, it depends on the size of the system. It can only be changed by two different modes: Work, W, and Heat, Q, trough the boundary of the system.

Work and Heat

Heat can be viewed as a disordered way of transferring energy (caused by temperature gradient across the boundary) while work is an order way of transferring energy (lifting a weight for instance)

The 1st Law of Thermodynamics

The internal energy of an isolated system is constant. If the system is closed it can only be transferred by heat flow or work done.

In differential form

In integrated form:

dQ and dW are not exact differentials what means that they will depend on the path! So heat and work are path functions, they are associated with a process, not a state.

The 1st Law of Thermodynamics

An equivalent formulation of the first law is the following: the work necessary to change an adiabatic system from one state to another is always the same, no matter the type of work done.

The 1st Law of Thermodynamics

But… AU is the same for all the processes!

Signal convention

Work

Expansion work

Let us assume the work done by the expansion of a gas against constant external pressure:

In a free expansion, against the vacuum, the external pressure is null (pext = 0), so W=0.

Isothermal Perfect gas expansion (1 step)

Isothermal Perfect gas expansion (two steps)

Isothermal Perfect gas expansion (Infinite steps)

If at each step we have p = pext, we have infinite expansions, and maximum work is delivered to the surroundings! This is obtained using a reversible path.

Reversible Process

Considering the reversible expansion of a perfect gas, he have:

R = 8.314 J.K-1.mol-1

(T, p1, V1) (T,p2,V2) (T,p1,V1)

Process I: expansion against pext = p2 and compression with pext = p1

expansion

compression

Work done to System!

Process II: infinite expansions and compressions with pext = palong the path

Reversible Process!

It’s the quantity flowing between the system and the surroundings that can cause a change in temperature of the system and/or the surroundings. Like work, heat its not a state function!

What connects Heat with temperature it’s the Heat capacity, C. Units SI are J.K-1.mol-1.

At constant volume:

At constant pressure:

At constant volume, dw = 0 so, from the 1st Law, we can easily obtain:

Chemical reactions and many other processes, including biological, take place under constant pressure and reversible pV work. Let us define a new function of state, the enthalpy, defined as:

Differentiating:

At constant pressure:

Previous result shows that the enthalpy its equal to the heat in a constant pressure process, and we can finally obtain:

We can now derive a relation between Cp and Cv for an ideal gas:

Assume this is equal!

But, H = U + pV =U + RT (per mole)

For instance, for an ideal monatomic gas CV =3/2 R , so Cp = 5/2 R

Let us consider the free expansion of a gas, to get

Adiabatic, q = 0

Expansion into the vacuum, w = 0

P~0

The experiment proofs that, for an ideal gas, U = U(T)!

If we regard the internal energy function as U =U(V,T) , then the total differential of U comes:

For an ideal gas so dU = CvdT

This means that the internal energy of an ideal gas depends only on temperature. As a consequence: ΔU = 0 for all isothermal expansions or compressions of an ideal gas, and

For any ideal gas change of state.