Thermodynamics

Thermodynamics (Division C) and Keep the Heat (Division B) are slated as national events in the 2011-2012 season. Keep the Heat was formerly run as a trial event in Minnesota, replacing Egg-O-Naut because Minnesota winters are too cold to run outdoor events involving liquid water.

Overview
In this event you create a model or device that simply insulates a 250ml Pyrex beaker filled with 100ml of hot water. Your goal is to create a device that loses the least amount of heat after a period of time determined by the instructor (20-30 minutes). While your device is being tested you take a short test on heat (conversions, specific heat, etc). The starting temperature can be anything from 50 degrees Celsius to 90 degrees Celsius (determined by the instructor). Participants will also need to estimate the amount of heat lost according to graphs made prior to the competition (see "Construction").

Device
The Thermo Lab device must fit inside a 30cm cube. If it does not fit, the device will be disqualified. The beaker must be a 250ml Pyrex beaker and it must be easily removable. There should also be easy access to the interior of the device for temperature measurement by the instructor. Plugs are allowed as well as covered loose fiberglass.

Documentation
Prior to the competition, competitors should make cooling curve graphs for various starting temperatures so they can easily identify the final temperature at the competition.

Test
The Thermo Lab test can have many different things on it. A Thermo Lab test may include (but is not limited to): temperature conversions, definitions of heat units, heat capacity, and specific heat calculations. No notes or resources may be used on this test. You are allowed a nonprogrammable-nongraphing calculator.

Basic Thermodynamics
Thermodynamics is the study of thermal energy along with how it interacts with matter and energy (Another definition is Lord Kelvin's, and that is: "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency.")

The Four Laws of Thermodynamics
There are four basic laws of thermodynamics that apply to any situation that meets the requirements of the specific law (Although the laws actually start with the zeroth law and end with the third since the zeroth law was created later).

Zeroth Law of Thermodynamics: "If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other."


 * This law is rather self explanatory, but it can be represented in math as: if $$a=c$$ and $$b=c$$, $$a=b$$.

First law of thermodynamics: "A change in the internal energy of a closed thermodynamic system is equal to the difference between the heat supplied to the system and the amount of work done by the system on its surroundings."


 * This basically means that if a closed system receives more net heat than net work that it does, it would gain internal energy, and if the net work exceeds net heat intake, the closed system would lose energy (This can be represented in mathematics where i=change in internal energy, q=net heat intake, and w=net work as: $$i=q-w$$, and that means that when $$q>w$$, $$i>0$$. In addition, $$i<0$$ when $$q<w$$, and $$i=0$$ when $$q=w$$.) One factor that supports this law is the Law of conservation of Energy.

Second Law of Thermodynamics: "Heat cannot spontaneously flow from a colder location to a hotter location."


 * This law explains entropy in that as the temperature of one object nears the temperature of another object, the amount of entropy increases increases, and this entropy must be decreased in order for work to be done. One example for this is a steam engine. As a steam engine is used, the metal and water in the steam engine will retain heat until the temperature of the metal and water is equivalent to the temperature of the fire that they are above. This waste heat can be removed by either the usage of cooling water or shutting the steam engine down until it cools down to a fair temperature.

Third Law of Thermodynamics: "As a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value."


 * The importance of this law is that it proves that it is impossible for an object reach absolute zero. The reason for this is that as an object reaches lower temperatures, the molecular/atomic process slow which decreases heat transfer while the amount of work done (In this case it is molecular in the form of heat transfer.) decreases in an asymptotic approach and exponential decay due to the First and Second Laws of Thermodynamics. One example of this is that if there was an object at absolute zero touching another object that is significantly warmer, the warmer object would lose temperature in ever decreasing amounts as there is less energy for the warmer object to give to the colder object (The colder object also gains energy due to the Law of Conservation of Energy and would have less of a potential to receive energy.). That allows both of the objects' temperatures to be tracked using an exponential decay graph for the warmer object and a graph of exponential growth for the colder object (with temperature as the y axis and time as the x axis), and both graphs would have an asymptotic approach toward a certain temperature value (This situation is like constantly dividing 1,000,000 in half in an attempt to reach zero.). That means that an object can never be at absolute zero unless an object can be at a temperature lower than that (which is impossible due to the definition of absolute zero). This also implies that two objects that start out at different temperatures will never reach exactly equal temperatures, but measurement tools don't necessarily have the accuracy to detect those small differences. In addition, the way heat transfers between objects is dependent on the composition of the objects that the heat is going between.

Note: The wording of the laws is the specific wording used in the Wikipedia article for thermodynamics.

Carnot Cycle
One of the important things that helped with the creation of the Four Laws of Thermodynamics is the Carnot Cycle. A picture of the Carnot Cycle is shown below. In the above image, Q stands for heat, and W stands for work. What is happening in the picture is that heat is being transferred from the warmer red square (at temperature $$T_1$$) to the neutral white square where some of the heat remains in the form of work. The rest of the heat moves to the colder blue square (at temperature $$T_2$$). Due to the Law of Conservation of Energy (which has the implication that energy can't be created or destroyed and is sometimes stated as that), the amount of work done in the middle square must be equivalent to the heat transferred from the red square to the white square minus the heat transferred from the white square to the blue square. That can be mathematically represented as: $$W=Q_1-Q_2$$. In addition, the amount of heat transferred and the amount of work done are proportional to temperature by the equation $$W=(1-T_2/T_1)\cdot Q_1$$. This makes logical sense in that as the temperatures of two objects near each other, the potential and amount of heat transfer decreases which would also decrease the amount of work done on the white square due to the Second and Third Laws of Thermodynamics. In addition, that equation can be altered so that you can find $$Q_2$$. The new equation would be: $$Q_2=(T_2/T_1)\cdot Q_1$$. That can be further altered to show the proportion between temperature difference and heat transfer, and the equation for that is: $$Q_2/Q_1=T_2/T_1$$. That can then be written as $$0=T_2/T_1-Q_2/Q_1$$, and then it can be changed to $$0=Q_1/T_1-Q_2/T_2$$. Since $$Q_2$$ is a measure of heat output from the white square, it can be written as a negative number by using the white square as a reference point. That means that the equation can be turned into the inequality $$Q_1/T_1+Q_2/T_2>0$$ or the equality $$S=Q_1/T_1+Q_2/T_2$$ (where S equals entropy). The function of that equation and the inequality is entropy since it represents the part that is not work in the equations $$W=Q_1-Q_2$$ and $$Q_1=W+Q_2$$, for it is based off of the equation $$Q_2=(T_2/T_1)Q_1$$. If you go back to the equation $$Q_2/Q_1=T_2/T_1$$, you can alter it so that you can find any of those variables, and the equations to do that are: $$Q_2=(T_2/T_1)\cdot Q_1$$, $$T_1=T_2\div (Q_2/Q_1)$$, $$Q_1=Q_2\div (T_2/T_1)$$, and $$T_2=(Q_2/Q_1)\cdot T_1$$.

Importance
Studies of the Carnot Cycle have caused the creation of the First and Second Laws of Thermodynamics. If you look at the equation $$W=Q_1-Q_2$$, you can see that it shows heat flow in and out of the white square in the picture, and work in thermodynamics refers to energy transferred to a system that changes the system. This was restated later as the First Law of Thermodynamics. If you look at the equation for finding entropy, $$Q_1/T_1+Q_2/T_2=S$$, and apply it to the Carnot Cycle while including the progression of time, you can see that as the Carnot Cycle goes on for longer periods of time, $$T_1$$ decreases towards $$T_2$$ which increases. In addition, $$Q_1$$ and $$Q_2$$ would decrease. This became the Second Law of Thermodynamics.

Examples of Usage
The equations in the Carnot Cycle can be used to determine the values for all 6 of the variables so long as you have the value for one temperature variable, one heat variable, and one other variable that is not the value for entropy.

Lets suppose in the Carnot Cycle that $$W$$ is 10 joules, $$Q_1$$ is 40 joules, and $$T_1$$ is 400 degrees Kelvin. We can make a table of our information which is:

From there we can use formulas to find out the rest of the variables. The equation: $$Q_1=W+Q_2$$ can be used to find the value for $$Q_2$$. The equation with values for the variables is: $$40=10+Q_2$$, and that can be simplified to $$30=Q_2$$. The new table would therefore be:

Then, the equation: $$Q_2=(T_2/T_1)\cdot Q_1$$ can be used to find the value for $$T_2$$. The equation with values for the variables is: $$30=(T_2/400)\cdot 40$$. The equation can then be simplified to: $$0.75=T_2\div 400$$, and that can be simplified to: $$300=T_2$$. This answer can be verified by checking it with the equation: $$W=(1-T_2\div T_1)\cdot Q_1$$, and the equation with values for the variables is: $$10=(1-300\div 400)\cdot 40$$. That can be simplified to $$10=(1-0.75)\cdot 40$$ which is equal to $$10=0.25\cdot 40$$. That is equal to $$10=10$$ which means that $$225=T_2$$. Therefore, the new table is:

Finally, the equation $$S=Q_1/T_1+Q_2/T_2$$ can be used to find the value for S, and the equation with values for the variables is: $$S=40/400+30/300$$. That can be simplified to$$S=0.1+0.1$$ ($$S=2\cdot 0.1$$) which is equivalent to $$S=0.2$$. Therefore all of the values for the variables in a table is:

Joule's Laws
Joule's Laws are two laws created by James Prescott Joule that describe the heat dissipation of components in an electrical circuit and how the internal energy of an ideal gas relates to temperature, pressure, and volume.

Joule's First Law: "$$Q=I^2\cdot R\cdot t$$"


 * In that equation, Q is the heat dissipation of the component while I is the electrical current through the component, and R is the electrical resistance of the component while t is the time that the electricity ran through the component. If the time is measured in seconds (s is oftentimes used as the variable for seconds.), the variable Q will represent an answer in Joules (j). Joule's first Law provides one way in which Electrical Engineering and Thermodynamics relate. In Electrical Engineering, the equation for finding the power in a circuit/component is: $$P=V\cdot I$$ (where P is power in watts, V is volts, and I is current or amperes.) which can be written as $$P=I^2\cdot R$$ (where R is the electrical resistance). That means that: $$J=P\cdot s$$ (W can also be used in place of P.). This can be further proven by one definition of a volt ($$V=J\div C$$ where C represents Coulombs). One Ampere (amp) is equivalent to one Coulomb per second which means that the equation can be changed to: $$V=J \div (I\cdot s)$$ or $$J=V\cdot I\cdot s$$ which is equal to $$J=P\cdot s$$. The main importance of Joule's First Law is that it allows people to calculate the heat dissipation of electrical circuits/components.

Joule's Second Law: "The internal energy of an ideal gas is independent of its volume and pressure, depending only on its temperature."

Note: The wording of the laws is the specific wording used in the Wikipedia article for Joule's Laws.

Thermodynamic Systems
A thermodynamic system is region of the Universe with specific boundaries that is analyzed using thermodynamic theories, principles, and laws.

Everything that is not part of a thermodynamic system is said to be in the surroundings. The system and surroundings are separated by a boundary that may be fixed (always stays in the same spot), movable (location can change), imaginary (There is nothing separating the surroundings and the system, and the boundary is merely a designated space.), or real (The boundary is a physical object.)

There are three types of thermodynamic system, and each type allows different things to pass through the boundary. The types are:

Open System: In open systems, matter, heat, and work can cross the boundary to enter or exit the system. The First Law of Thermodynamics when applied to an open system is (quoting from Wikipedia): "the increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system."

Closed System: In a closed system, heat and work can cross the boundary, but matter can't cross the boundary. In addition, there is a type of boundary that may be in a closed system that heat can't cross, adiabatic, and one that work can't cross, rigid.

Isolated system: In an isolated system, neither matter, heat, or work can cross the boundary. Therefore, differences in thermal energy will typically lessen until the system reaches thermodynamic equilibrium.

Branches of Thermodynamics
There are several branches of thermodynamics, and each branch is about a specific aspect of thermodynamics.

Classical Thermodynamics

 * This is thermodynamics on a large or macroscopic scale. This branch of thermodynamics is used to model states and processes that are based on properties that can be measured, defined, and examined in a laboratory. These models include models based on the Four Laws of Thermodynamics and include: energy, mass, work, and heat exchanges.

Statistical Thermodynamics

 * This is thermodynamics on the molecular/atomic scale. This branch of thermodynamics explains how microscopic events, properties, and interactions influence Classical Thermodynamics.

Chemical Thermodynamics

 * This branch of thermodynamics is about how energy, within the subject of thermodynamics, influences chemicals and chemical reactions.

Equilibrium Thermodynamics

 * This branch of thermodynamics is about how matter and energy in a system change as the system approaches thermal equilibrium. One main goal in Equilibrium Thermodynamics is to figure out what a system will be like when it reaches thermodynamic equilibrium if you know the starting parameters for the system and the laws/forces that will act upon it.

Non-Equilibrium Thermodynamics

 * This branch of thermodynamics is the study of systems that aren't in thermal equilibrium, and many of the laws/theories/concepts are more general than the ones in Equilibrium Thermodynamics.

Conversions and Equations
This is an organized list of the ways to find different variables and convert from one unit to another (for convenience so that people don't have to look all through the article to find this information).

Conversions
This is a list of unit conversions.

Joule
Ways to convert other energy units into a Joule.


 * 1) Multiply British Thermal Unit amount by 1,055 to get an approximation of the energy in Joules.
 * 2) Multiply Small Calorie amount by 4.2 to get an approximation of the energy in Joules.
 * 3) Multiply Large Calorie amount by 4,200 to get an approximation of the energy in Joules.

British Thermal Unit
Ways to convert other energy units into British Thermal Units.


 * 1) Divide the amount of Joules by 1,055 to get an approximation of the energy in British Thermal Units.
 * 2) Multiply Small Calorie amount by 0.003981042 to get an approximation of the energy in British Thermal Units.
 * 3) Multiply Large Calorie amount by 3.981042654 to get an approximation of the energy in British Thermal Units.

Small Calorie
Ways to convert other energy units into Small Calories.


 * 1) Divide the amount of Joules by 4.2 to get an approximation of the energy in Small Calories.
 * 2) Multiply Large Calorie amount by 1,000 to get the amount of energy in Small Calories.
 * 3) Multiply the British Thermal Unit amount by 251.1904762 to get an approximation of the amount of energy in Small Calories.

Large Calorie
Ways to convert other energy units into Large Calories.


 * 1) Divide the amount of Joules by 4,200 to get an approximation of the energy in Large Calories.
 * 2) Divide Small Calorie amount by 1,000 to get the amount of energy in Large Calories.
 * 3) Multiply British Thermal Unit amount by 0.251190476 to get an approximation of the amount of energy in Large Calories.

Kelvin
Ways to convert other temperature units to Kelvin


 * 1) Add 273.15 to the Celsius amount to get the temperature in Kelvin.
 * 2) Add the Fahrenheit temperature to 459.67 and then multiply it by 5/9 to get the temperature in Kelvin.

Fahrenheit
Ways to convert other temperatures to Fahrenheit.


 * 1) Multiply the Kelvin temperature by 9/5 and then subtract 459.67 to get the temperature in Fahrenheit.
 * 2) Multiply the Celsius temperature by 9/5 and then add 32 to get the temperature in Fahrenheit.

Celsius
Ways to convert other temperatures to Celsius.


 * 1) Subtract 273.15 from the temperature in Kelvin to get the temperature in Celsius.
 * 2) Subtract 32 from the Fahrenheit temperature and then multiply it by 5/9 to get the temperature in Celsius.

Equations
This is a list of equations that define certain variables (Electrical Engineering variables are not included since heat dissipation of components is a minor point.).

Joule
Equations that define a joule (J) include:


 * 1) $$J=I^2\cdot R\cdot s$$
 * 2) $$J=M\cdot m$$
 * 3) $$J=kg\cdot m^2\div s^2$$
 * 4) $$J=P\cdot s$$
 * 5) $$J=V\cdot I\cdot s$$
 * 6) $$J=V\cdot C$$

Work
Equations that define work (W)


 * 1) $$W=Q_1-Q_2$$ (from the Carnot Cycle)
 * 2) $$W=(1-T_2/T_1)\cdot Q_1$$ (from the Carnot Cycle as well)

Entropy
Equations that define entropy (S) include:


 * 1) $$S=Q_1/T_1+Q_2/T_2$$ (from the Carnot Cycle)

Heat
Equations that define heat (Q, $$Q_1$$, and $$Q_2$$).


 * Q
 * 1) $$Q=I^2\cdot R\cdot t$$ (from Joule's Laws)
 * 2) $$Q_1$$
 * 3) $$Q_1=W+Q_2$$ (from the Carnot Cycle)
 * 4) $$Q_1=W\div (1-T_2/T_1)$$
 * 5) $$Q_1= Q_2\div (T_2/T_1)$$
 * 6) $$Q_1=(Q_2/T_2)\cdot T_1$$
 * 7) $$Q_2$$
 * 8) $$Q_2=Q_1-W$$ (from the Carnot Cycle)
 * 9) $$Q_2=(T_2/T_1)\cdot Q_1$$
 * 10) $$Q_2=(Q_1/T_1)\cdot T_2$$

Temperature
Equations that define temperature ($$T_1$$ and $$T_2$$).


 * 1) $$T_1$$
 * 2) $$T_1=Q_1\div (Q_2/T_2)$$ (from the Carnot Cycle)
 * 3) $$T_1=T_2\div (Q_2/Q_1)$$
 * 4) $$T_2$$
 * 5) $$T_2=Q_2\div (Q_1/T_1)$$ (from the Carnot Cycle)
 * 6) $$T_2=(Q_2/Q_1)\cdot T_1$$

Vocabulary
Internal energy: The energy of the motions of atoms and molecules within an object (includes potential energy of molecules and atoms in liquids and solids). Temperature is the measure of the internal energy of an object.

Entropy (when applied to thermodynamics): The amount heat that can't be used to do work.

Absolute Zero: The temperature at which all processes stop (defined in the third law of thermodynamics). This temperature is: 0 degrees Kelvin, -273.15 degrees Celsius, or -459.67 degrees Fahrenheit.

Thermal Equilibrium: When an object/system has an unchanging uniform temperature or when there is no exchange of heat when two objects/systems can exchange heat (In other words, they have the same temperature.).

Thermodynamic Equilibrium: When there are no net flows of matter or energy to or away from a system and no net changes in the matter and energy in that system.

Joule (J): A unit of work equal to: $$N\cdot m$$, $$(kg\cdot m^2)\div s^2$$, $$P\cdot s$$, $$V\cdot I\cdot s$$, $$V\cdot C$$, and $$I^2\cdot R\cdot s$$ (where N=Newtons, m=meters, kg=kilograms, s=seconds, P=watts, V=volts, I=amperes, C=Coulombs, and R=resistance in Ohms.).

Work (Thermodynamics while the variable W is typically used): The energy transferred between systems that changes the system that it is transferred to (measured in joules).

Heat (Q): Energy that is transferred from one system to another in the form of internal energy due to differences in temperature. Can be measured in joules, British Thermal Units, small calories, or large calories. When it is a rate, watts is oftentimes used.

British Thermal Unit (abbreviated as BTU): Roughly 1,055 joules or the amount of energy needed to get one pound of water from 39 to 40 degrees Fahrenheit.

Small Calorie: The amount of energy required to increase the temperature of one gram of water by one degree Celsius (about 4.2 joules).

Large Calorie: The amount of energy required to increase the temperature of one kilogram of water by one degree Celsius (about 4,200 joules).

Volt (Voltage, V, E): The energy required to move electrons from one location to another divided by the charge of the electrons in Coulombs. Can be stated as: $$V=I\cdot R$$, $$V=J\div C$$, and $$V=W\div I$$.

Coulomb (C): The charge of an electrical current of one ampere in one second or the absolute value of the electrical charge of about 6.24*10^18 protons or electrons (with protons having a positive charge and electrons having a negative charge).

Ampere (Amp, I): The electrical charge of one coulomb in one second (mathematically: $$I=C\div s$$)

Resistance: The amount that an object resists the flow of electric current (found using: $$R=V\div I$$)

Watt (P or W): The Electrical Engineering unit for power that is equivalent to one joule per one second or one volt in a current of one ampere ($$P=J\div s$$ and $$P=V\cdot I$$).

Links
http://www.minnesotaso.org/Files/KEEP%20THE%20HEAT.pdf

Wikipedia-Thermodynamics

Hyperphysics-Thermodynamics

Wikipedia-Joule's Laws

Wikipedia-Entropy