Basic Thermodynamics Chapter 2

We’ve been here before  The material in this chapter is a brief review of concepts covered in your Introductory Engineering Thermodynamics class  Some of the conventions are different, and all of the material is worth reviewing

ME and ChE viewpoints are different  Mechanical engineers almost always deal with pure substances Steam Air Refrigerants  Chemical Engineers are interested in: Mixtures Reacting systems

 ME’s are interested in devices that produce or consume work Engines Refrigeration systems  ChE’s use devices to produce or separate chemical compounds

 A small number of working fluids are used in most processes of interest to ME’s  ChE’s use a wide variety of process feeds and create an even wider variety of products

Balance Equations Accumulation = creation – destruction + flow in – flow out Expressed as a rate: Accumulation = creation – destruction + flow – flow rate rate rate rate in rate out This is called the GENERAL Balance Equation

Mass Balances  Mass can neither be created nor destroyed  Antoine Lavoisier Tax collector Beheaded during the French Revolution Accumulation = creation – destruction + flow in – flow out

Balance equations without creation or destruction terms are called conservation equations Or expressed as a rate:

Remember, mass is conserved, but moles are not 3H 2 + N 2 ⇋ 2 NH 3 6g + 28g = 34g 3mole + 1mole ≠2 mole If there are no reactions, you can use either kg or moles

Energy  Energy is neither created nor destroyed  Creation = Destruction =0 Or expressed as a rate:

Kinds of Energy  There is only one kind of mass, but energy exists in many forms  Macroscopic Kinetic (KE) Potential (PE)  Microscopic Internal Energy (U) For most chemical engineering applications kinetic and potential energy are zero.

Energy Balances How can energy get into or out of a system? Heat, Work and Energy Transfer with Mass

Let’s Look at Closed Systems First  There is no mass transfer into a closed system  The only way energy can get into or out of a closed system is by heat transfer or work

Conventions  Mechanical Engineers are interested in creating devices that produce work For them it makes sense that work out is positive  Chemical Engineers use work to run devices – they have to pay for the work they consume For them it makes sense that work in is positive

This book…  Work in is postive  Heat in is positive Remember – this only applies to closed systems

Now we can move on to Control Volumes  How are control volumes different from closed systems?  What effect does this have on the energy balance? Energy can flow in with the matter

Total Energy of a flowing fluid The fluid possesses an additional form of energy – the flow energy (flow work) Methalpy

Energy Balance for a Control Volume at Steady State

Rewrite

Two Simplified Cases of the Energy Balance  Closed system  Control volume at Steady State

Second Law of Thermodynamics  Intuitively the easiest to understand  We understand that most processes only run in one direction without outside intervention

 The second law of thermodynamics states that processes occur in a certain direction, not in just any direction.  Physical processes in nature can proceed toward equilibrium spontaneously:

Water always flows downhill

Gases always expand from high pressure to low pressure

Heat always flows from high temperature to low temperature

We can reverse these processes  It requires the expenditure of work  The first law gives us no information about the direction in which a process occurs – it only tells us that energy must balance  The second law tells us in which direction processes occur

Work Always Converts Directly and Completely to Heat, But not the Reverse © The McGraw-Hill Companies, Inc.,1998 Work and Heat are not interchangeable forms of energy We need a device to convert heat to work

Entropy  Studied entropy in some detail in Thermo I True for reversible processes in a closed system

Entropy Generation Entropy transferred with Heat Transfer, not necessarily reversible Entropy flowing into and out of the system Entropy Accumulation Irreversible Processes  Irreversible processes create entropy  Entropy is not a conserved quantity This is a balance equation – not a conservation equation

For a closed system

For a control volume at steady state

Convenience Properties  We’ve already introduced enthalpy  Gibbs Free Energy  Helmholz Free Energy If you wanted to, you could do all thermodynamic calculations with just u and s

Using the First and Second Laws  We’ve used these laws before Looked up values of properties Calculated values of properties  This was easy if we had a common material such as steam, or we had an ideal gas

Life gets harder…  If there is no easy way to find table  If we are using mixtures of gases or liquids But let’s talk about the “easy” stuff first

Reference States  Usually we only care about changes in u, h and s  That means we don’t need to know the absolute value of the property, and can assign an arbitrary reference state

For example, for steam  u = 0  s = 0  for the saturated liquid at the triple point of water

Other common references Refrigerants u=s=0 at -40 F Hydrocarbons u=s=0 at 0 K Different tables may use different reference states – don’t combine table information, unless you’re sure they are consistent with each other

Measuring Properties  We can measure T P V m  There is no known direct measurement of u s All values of u and s are based on calculations from the measurable quantities

Work and Heat  The defining equation for changes in energy involves both work and heat  The defining equation for changes in entropy involves heat

You can’t measure either directly  From mechanics  But heat isn’t that easy Joule demonstrated the mechanical equivalence of heat (pg 31) Heat is usually measured in a calorimeter, which requires the use of heat capacity data

Heat capacity  Energy required to raise one unit mass one degree  Function of temperature

C, C v, C p  It takes more energy to raise the temperature of a gas at constant pressure, than at constant volume  C p > C v for gases C p –R = C v  C p = C v for liquids

Do you remember deriving these in Thermo I ? Don’t forget that C v and C p are both functions of temperature At constant pressure

The T-ds relations Consider an internally reversible process

First Gibbs equation or First Tds relationship Or… To find  s all you have to do is integrate!!!

2 nd Gibbs relationship Recall that… Find the derivative, dh Rearrange to find du

First Tds relationship Second Tds relationship, or Gibbs equation To find  s all you have to do is integrate

We have two equations for ds To find  s, integrate the equation that is the easiest, or for which you have the data

We derived this for a reversible process  But… thermodynamic properties are state functions  It applies whether or not the process is reversible

So now we have equations for u, h and s – in terms of the measurable properties… P, T, v and m

Equations of State  State Postulate If you know two independent state properties – the state is defined  The most common equation of state (EOS) is the ideal gas law

Be careful!!  In Mechanical Engineering texts, R is considered to be a gas property  In this text, R is the same as R u – the universal gas constant  We could also write: where v is the volume per mole

In Thermo I, and in Process Engineering, we have studied other EOS  Van der Waal  Virial  Beattie-Bridgeman  Benedict Webb Rubin  Corresponding States Be sure to look over the discussion of these equations in our text

Corresponding States z is a function of relative temperature and relative pressure

How well these equations represent reality depends on the conditions Deviation of Predictions from the ideal gas law for Steam

Percentage Error for Nitrogen

Departure Functions  The compressibility factor is a simple example of a departure function Use as simple a model as possible Predict the departure from the simple model

Widely used departure functions  For pure species gases Enthalpy departure Ideal gas prediction Actual

Widely used departure functions  For pure species gases Enthalpy departure Entropy departure Predicted Actual