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ME 200: Thermodynamics I

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Thermodynamics

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Students who study thermodynamics often find it to be one of the most challenging subjects, especially at more advanced levels where calculus is an integral part of the topic.  It is, however, an important topic in both Physics and Chemistry and is something that all physical scientists, engineers, and even many biologists study.

Thermodynamics is the study of Heat and Energy.  Many people use the terms "heat," "energy," and "temperature" interchangeably, but heat is actually one type of energy and temperature represents another type of energy.

Energy Transformation

The first law of thermodynamics is that energy cannot be created or destroyed.  While this law is always true, energy can be transformed from one type to another.  Heat can be changed into kinetic (moving) or latent/potential (stored) energy.  Thermodynamics uses P-V-T (pressure, volume, and temperature) diagrams to model these transformations.

Heat Transfer

Heat can also be transferred from one object to another. This transfer can occur in one of three ways: conduction (by touching), convection (through a fluid), or radiation (as E&M Waves).  Thermodynamics studies these transfers on a macroscopic (object to object) scale and a molecular (atom to atom) scale.  Thermodynamics incorporates the mathematics involved in each of these types of heat transfer including Newton's Law of Cooling and the Stefan-Boltzmann and Wien Laws.

Some of the topics you can expect to see in more detail in your Thermodynamics course:

*  The work-energy theorem

*  Conservation of energy

*  Thermal expansion

*  The ideal gas law

*  Entropy, free energy, and enthalpy

*  Open and closed systems

*  Temperature and kinetic theory

*  Equilibrium

*  Different types of thermodynamic systems

In thermodynamics courses with a lab component, the first few labs all involve calorimetry and specific heat.  You can also expect to see some real world applications of these concepts including cryogenics, automotive angines, heat pumps & air conditioning systems, and even global climate systems.  Thermodynamics explains how to get a tight jar open and how to get a ring off your finger when it swells.  One particularly interesting application of thermodynamics uses Newton's Law of Cooling to determine time of death during forensic investigations.

The University of Notre Dame has an OpenCourseWare offering in thermodynamics that is an excellent tutorial for college students called Thermodynamics . Another great resource for college students would be MIT's OpenCourseWare offering called Thermodynamics of Materials .

Below, we'll briefly delve into two of the first thermodynamics concepts students encounter in their Physics classes - the work-energy theorem and conversation of energy.

• The Work-Energy theorem:

Every time motion is transmitted from one body to another by means of a force, an essential role is played by a physical quantity that we call work ( W ). By definition the work done by a force (acting on a body) of which the point of application moves with a distance (d) is equal to the scalar product between the two vectors representing the force and the displacement (the direct product between the two vectors through the cosine of the angle between them:

In the international system of units ( SI ) work is measured in Joules ( J ). One Joule is equal to the work done by a 1 Newton force, the application point of which moves 1 meter parallel with the force and in its direction. Thus if the force that acts on the body is opposing its motion, the work is always negative. 

Example 1:  Work Done by Gravity

The first instance is the work done by gravity on a falling body. Thus the work done by the gravity force is independent of the path taken by the body when falling and on how the body is moving in its fall, but is equal to the product between the weight of the body and difference of level ( H ) between the initial and final points:

Example 2:  Work Done by a Spring

The second instance is the work done by elastic forces when a spring is stretched or compressed. The elastic force always depends on the displacement from the equilibrium position, so that it is not constant (You may recall the formula for this: F ( x ) = -kx ).  Because the two quantities are directly related, calculating the total work requires an integral.  You can do so with the following formula:

Both the elastic force and the gravitational force are capable of doing work, the amount of which depends only on the initial and final points of the body motion.  The energy that is responsible for these types of work is called potential energy and the source of the work done by a body is the energy that it has.

• Transformations & Conservation of Energy

When work is done on a body, the body state changes between points A and B (that the body is moved). For this reason, the energy a body has is a physical quantity that depends on the state of the body and each of the points A and B correspond to a certain different energy. Mechanical energy has two parts: kinetic energy and potential energy.

Kinetic Energy

The energy that a body has that is due to its motion is called kinetic energy.  We define the kinetic energy of a body that is in translational motion with speed as being equal to half of the product between the mass of the body and its speed squared  (K.E. = 1/2 mv^2).  We can derive this by starting from the equation of the uniform accelerated motion using the following methods:

Thus, when a body is in motion, it can act on a second body doing work. This work is equal to the change in Kinetic Energy, as shown in the formula above where the variation of the kinetic energy of a body is equal to the work done by the force that acts on that body.

Gravitational Potential Energy

The potential energy describing the position of the body with respect to the earth is called gravitational potential energy. The gravitational potential energy is equal the mechanical work done by gravity (which we call weight) but has the opposite sign.

A body found at a greater height has a bigger potential gravitational energy.  So, when we bring a body to a greater height, we do work on it.  Gravity is also doing work on it, but this work is negative, since it is opposing the body motion.

Elastic Potential Energy

The potential energy describing the deformation of a spring with respect to its rest position is called elastic potential energy. Again, by convention, the potential elastic energy variation is equal and contrary to the work done by the elastic force:    

Note:  a spring either compressed or stretched has positive potential energy (because elastic forces always oppose the displacement X from the equilibrium position and thus do negative work) since P.E. = 1/2kx^2.

Conservation of Total Energy

Building off the idea that the change in kinetic energy is equal to the work done, we can write the following equation:

This is the Law of Conservation of Total Energy.  The total energy is the sum between its potential and kinetic energies, and it always remains constant if the body moves into a conservative field of forces.

If you are interested in experimenting with conservation of total energy, there are two very nice applets on the web that let you do this. To see work and gravitational potential energy in action go to Energy State Park , to experiment with springs and potential energy go to Masses and Springs . A good physics book for college where you can learn further about work and energy can be found on Amazon here.

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Thermodynamics is one of the branches of physics which is related to heat and temperature and their relationships with other forms of energy like chemical, electrical, or mechanical energy. It describes how different forms of energy are converted from or to thermal energy and how the matter of a substance gets affected through it.

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Thermodynamics is the part of material science that manages the connections among the heat and different types of energy. Specifically, it depicts how thermal energy is changed over to and from different types of energy and how it influences matter.

Heat energy can be moved to start with one body then onto the next or between a body and the earth by three distinct methods: conduction, convection, and radiation. Conduction is the exchange of heat energy through a strong material. Conduction between bodies happens when they are in direct contact, and particles move their energies over the interface.

The four laws of thermodynamics for Thermodynamics Assignment Help Online

The fundamental principles of thermodynamics were initially communicated in three laws. The issue, however, was that the initial three laws had just been built up and were notable. The new law the "Zeroth Law." In brief, these laws are:

The Zeroth Law states that if two bodies are in thermal equilibrium with some third body, then they are also in equilibrium with each other. This establishes temperature as a fundamental and measurable property of matter.

The First Law states that the total increase in the energy of a system is equal to the increase in thermal energy plus the work done on the system. This states that heat is a form of energy and is therefore subject to the principle of conservation.

The Second Law states that heat energy cannot be transferred from a body at a lower temperature to a body at a higher temperature without the addition of energy. This is why it costs money to run an air conditioner.

The Third Law states that the entropy of a pure crystal at absolute zero is zero. As explained above, entropy is sometimes called "waste energy," i.e., the energy that is unable to do work, and since there is no heat energy whatsoever at absolute zero, there can be no waste energy

The Zeroth Law : It expresses that on the off chance that two bodies are in thermal balance with some third body, at that point they also in equilibrium with each other. This sets up the temperature as a key and quantifiable property of the issue.

The First Law : It expresses that the total increase in the energy of a framework is equivalent to the expansion of thermal energy plus the work done on the framework.

i.e Change in Internal Energy = Change in Thermal Energy + Work done

The Second Law : It states that heat energy can't be moved from a body at a lower temperature to a body at a higher temperature without the expansion of energy. This is the reason it costs cash to run a climate control system.

The Third Law : It expresses that the entropy of an unadulterated precious stone at outright zero will be zero. As clarified above, entropy is in some cases called "squander energy," i.e., energy that can't accomplish work, and since there is no warmth energy at all at supreme zero, there can be no waste vitality

Sample of Thermodynamics Homework Help Solved

A) the generator.

What are the compositions of the two phases present in the lower reservoir of the generator? Be as specific as possible. How can you tell?

b) The Bubble Pump

Why does the bubble pump itself operate at 100 °C and how can you tell? Hint: It’s not the initially-obvious answer.

c) The Condenser/Absorber

What is the operating temperature of the condenser/absorber? What are the compositions of the two liquid phases present at the bottom of the Condenser/Absorber? Be as specific as possible. How can you tell?

d) The Evaporator

What is the minimum possible operating temperature of the evaporator? How can you tell? What are the compositions of the two phases present in the evaporator if the evaporator is operating at this minimum temperature? Be as specific as possible. How can you tell?

e) That long tube...

Why is it critical for the tube in the above prototype photo that runs from the top of the generator’s lower reservoir to the top of the evaporator to be angled upwards? What condition should be met by this component of the device?

Question 2: Explaining key phenomena by chemical potential/equilibrium

Why, in terms of chemical potential, does heating the ammonia/water(l) mixture enrich the vapor in ammonia and the liquid in the water? Use appropriate equation(s) to discuss this qualitatively.

b) The Condenser/Absorber

Why, in terms of equilibrium, does the falling film of water absorb the gaseous ammonia? Why does the butane condense (particularly since the operating temperature here is higher than it is in the evaporator)? Why do the two liquids form separate phases (discuss this point from the perspective of “regular solutions,” discussed in the textbook, and explain what must be true about the relative entropic and enthalpic contributions)?

c) The Evaporator

Using an appropriate expression for chemical potential, demonstrate that bubbling ammonia (g) through butane (l) at an overall pressure of 4 bar and a temperature above 265 K causes evaporation of the butane. Hint: Explain the process from the perspective of an ammonia bubble that enters the butane (l) environment.

Question 3: Ammonia-water equilibrium

A) ideal solution approximation.

i) Generate a plot of the vapor pressure of pure water and pure ammonia as a function of temperature over the temperature range that is relevant to the Einstein refrigerator.

ii) Generate a plot of the vapor pressures of the two components and the total vapor pressure as a function of mole fraction of ammonia assuming the mixture is an ideal solution (put this plot in a

Manipulate wrapper so that you can modify the temperature at which you are looking at this). Mathematica notes: Manipulates work much faster without built-in units.

iii) Generate a plot of the total vapor pressure as a function of mole fraction of ammonia in both the liquid phase and the gas phase (that is, the mole fraction of ammonia in the liquid phase is the x-axis of one graph, the mole fraction of ammonia in the gas phase is the x-axis of the second graph, both plotted on the same plot). Use the same type of Manipulate wrapper as you did for part (ii).

iv) The most useful version of this phase diagram has temperature vs. mole fraction at the specific operating pressure rather than pressure vs. mole fraction at a specific temperature. Unfortunately, solving the expressions you have already found for temperature is quite difficult (make sure you save before trying anything!). Nonetheless, I m going to walk you through doing it. Here is an approach that works:

First, set up a list of mole fractions running from 0 to 1 every 0.01. You will in the next few steps be finding the boiling point for these mole fractions each for the vapor mole fraction and the solution mole fraction.

In part (ii) you found an expression for the total vapor pressure at a particular temperature and solution phase mole fraction. You want to know at what temperature this vapor pressure equals the operating

temperature of the Einstein refrigerator. Unfortunately, Solve and NSolve don’t work. But FindRoot does. FindRootexpression, {var, var 0 } finds a value for variable “var” where “expression” equals zero, and it starts its search at var = var 0 . So you can solve an equation using FindRoot by simply taking the left-hand side of the equation minus the right-hand side, and using FindRoot. Use this approach to find the temperatures at which the total pressure equals the vapor pressure using the expression from part (ii) for all of the mole fractions you set up as a list in the previous step. This becomes the first line in your phase diagram.

Just like the last step, find the temperatures that have vapor pressures that equal the operating pressure of the Einstein refrigerator, using the expression you found in part (iii) when using the vapor-phase mole fraction as the x-axis. This becomes the second line in your phase diagram.

You now should have some densely-spaced data points for two curves for your phase diagram. Plot them on the same plot using ListLinePlot.

b) Interpretation

i) The graphs you generated in part (a) (i) through the part (a) (iii) should beat you over the head with one significant take-home message. What is it?

ii) The final graph you generated in part (a) should look similar to the first graph for reference above. Identify any noteworthy differences between these two graphs and discuss how those differences result from the ideal solution approximation. Be specific.

Question 4: Some strange hypotheticals

A) semi-permeable membrane.

An enterprising engineer wants to improve the efficiency of the water/ammonia separation in the generator by covering the inlet to the bubble pump with a semi-permeable membrane that allows water to pass but blocks the passage of ammonia (assume such a membrane exists). How would such a change modify the operation of the refrigerator? Be quantitative in your answer, but assume ideal solution behavior where appropriate.

In constructing an Einstein refrigerator, a careless graduate student used tap water instead of deionized water. Qualitatively predict the effects of the ionic contaminants on each relevant physical process in the system, and draw a conclusion about the effect this would have on the overall functioning of the refrigerator.

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