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Chapter 1: The 1st Law of Thermodynamics

Table of Contents

Thermodynamics Vocabulary...................................................................................................... 2

The 1st Law of Thermodynamics ................................................................................................. 3 Energy ............................................................................................................................................. 3 Heat transfer .................................................................................................................................... 4 Work ............................................................................................................................................... 4 Power .............................................................................................................................................. 6 Example ......................................................................................... Error! Bookmark not defined. Example .......................................................................................................................................... 8 Example ......................................................................................... Error! Bookmark not defined.

Drawing Energy Flow Diagrams (EFDs) .................................................................................... 7 Example ......................................................................................... Error! Bookmark not defined. Example .......................................................................................................................................... 9 Example ......................................................................................... Error! Bookmark not defined. Example ......................................................................................... Error! Bookmark not defined. Example ........................................................................................................................................ 10

   

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Thermodynamics Vocabulary Thermodynamics is energy accounting. It is the study of how energy deposits and energy withdrawals change the total energy of a system.

In thermodynamics, the system is the entity we choose to analyze. It is closely related to what we’re asked to find, and is always associated with some quantity of mass.

The surroundings are everything that are not the system. The surroundings usually encapsulate the system, but can be inside it—think of a fluid flowing through an annular tube.

The system and the surroundings are separated by the system boundary. Both energy and mass can cross the system boundary, moving in to or out of the system (or both).

We use properties to describe what is happening in a system. A property is a characteristic of a system (because of its mass) that is independent of the system history. Examples of properties

include temperature (T), pressure (p), volume (V), energy (E), mass (m), and density (.

Properties can be intensive, extensive or specific. Intensive properties are independent of the

system size. Examples of intensive properties include T, p and . Extensive properties depend on the system size. Examples of extensive properties include V, E, and m. [Note that extensive properties are denoted by upper case letters, except for T, while intensive properties are denoted by lower case letters.

When extensive properties are normalized by mass, they become specific (a form of) intensive properties. For example, specific volume is:

Mass entering, w/energy

Energy transfer

due to Tsys->surr≠0

Mass exiting, w/energy

Energy transfer due to F∙ds

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A state is a set of properties that completely describes the condition of a system. A thermodynamic process describes the change a system undergoes from one state to another. A path is the series of states through which a system passes during a process (1>2 below).

The 1st Law of Thermodynamics The 1st Law of Thermodynamics is:

, ,

In words, the rate of change of energy within a system is equal to the net rate of heat transfer to

the system from the surroundings ( ), minus the rate of work done by the system on the

surroundings ( ), plus the rate of energy added as mass enters the system ( , ), minus the

rate of energy lost as mass exits the system ( , ).

Energy There are three forms of energy: kinetic energy ( ), potential energy ( ) and internal energy ( ).

Kinetic energy (KE) is system energy due to its motion. The change in kinetic energy is calculated from an object’s mass ( ) and initial and final speeds ( and ):

Potential energy (PE) is system energy due to its position. The change in potential energy is calculated from an object’s mass, the acceleration of gravity ( ), and the object’s initial and final height ( and ).

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Internal energy (U) is the energy associated with chemical bonds, nuclear motion, and electronic motion. We represent the change in internal energy as .

Energy can be stored in systems, can be converted from one form to another, can be transferred between systems or between the system and the surroundings, but is always conserved during all conversions and transfers.

Returning to the 1st Law, the rate of change of energy within a system can be expressed as the rate of change of the system’s kinetic, potential, and internal energy:

, ,

Heat transfer Heat transfer ( ) is energy transferred due to a temperature difference. Heat transfer always occurs from hot to cold, from a higher temperature region to a lower temperature one.

As a consequence, energy is transferred to a system when its temperature is exceeded by that of the surroundings. Energy is transferred from a system when its temperature is greater than that of the surroundings.

Heat transfer occurs in three forms: conduction, convection, and radiation. Conduction is heat transfer through direct physical contact. Convection is heat transfer due to the movement of fluids. Radiation is energy emitted by matter and requires no intervening medium to propagate.

Heat transfer will be positive when energy is transferred to the system (i.e., when the surroundings are hotter than the system). Heat transfer will be negative when energy is transferred from the system (i.e., when the system is hotter than the surroundings).

An adiabatic process is one in which there is no heat transfer.

Work Recall that W is the vector dot product of force and displacement.

∙

Of particular interest in thermodynamic systems is moving boundary work, or simply boundary work. Boundary work is the work done when the volume of a fluid changes by expansion or compression. Note that a fluid can be either a liquid or a gas.

Consider a fluid at pressure contained within a piston-cylinder device. The piston has cross-

sectional area . The fluid exerts a force on the piston of .

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The work done as the piston moves from position to position is:

∙

In order to integrate this expression, we need to know how pressure varies with displacement and how area varies with displacement. It is much more common in Thermodynamics to know how pressure varies with volume. Luckily, the product gives us the differential volume, . Therefore, our expression for boundary work is:

It is often useful to visualize boundary work by plotting the thermodynamic path on a pV diagram, where the work is the area under the curve.

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The p-V diagram also helps us understand the sign convention for boundary work. is

positive during expansion (volume increases as we move left to right on the p-V diagram) and negative during compression (volume decreases as we move right to left on the p-V diagram).

We will apply this sign convention whenever we discuss energy transfer by work. Work will be positive when the system does work on the surroundings and will be negative when the work is done on the system by the surroundings.

The general expression for work can also be used to calculate rotating shaft work, spring work, and electrical work.

Form “Force” “Displacement” Expression for work Moving boundary

Pressure Volume

Rotating shaft Torque: Angular displacement:

Hookean spring Spring force:

Deformation:

Electrical Voltage: (or is it ?)

Charge: ∆

Power Power is the rate of energy transfer by work. The most general expression for power is the vector dot product of force and velocity:

∙

The general expression for power can be used to calculate rotating shaft power and electrical power. There are special cases when the torque and voltage are steady (constant in time).

Form “Force” “Velocity” Expression for work

Rotational shaft Torque: Angular velocity:

Electrical Voltage: Current:

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Drawing Energy Flow Diagrams Energy Flow Diagrams (EFDs) show how energy is transferred, stored, and/or converted during a thermodynamic process. The steps to drawing an EFD are as follows:

1. Choose your system. Reading the find portion of the problem statement usually helps 2. Draw the system boundary. It separates the system from the surroundings. 3. Consider each term in the 1st Law and annotate the EFD accordingly:

a. Is there any change to the kinetic, potential, or internal energy within the system?

b. Is there any heat transfer crossing the system boundary? Look for T between the system and surroundings and the words “adiabatic” or “insulated.”

c. Is the any work being done by or on the system? Consider the four forms of work discussed previously (boundary, rotational shaft, spring, and electrical) and eliminate those that aren’t present. Rigid systems can’t have moving boundary work.

d. Is there any energy being transported into or out of the system by mass flow?

, ,

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Example An unknown ideal gas with a molecular weight of 36 g/mol undergoes a process following

, with n=1.67. The initial temperature is 250 °C and the initial pressure 1.7 bar. The specific volume increases by a factor of 2.4.

a) Calculate the final gas temperature. Report your answer in °C. b) Calculate the final gas pressure. Report your answer in bar.

Calculate the boundary work done during the process. Report your answer in kJ/kg.

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Example For the cast iron skillets below, draw EFDs for the skillet being preheated (energy transfer from above) and the preheated skillet being used for cooking (energy transfer from below).

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Example A residential sump pump is used to keep a below ground basement from flooding after periods of heavy rain. The electrically powered pump has a water inlet at the bottom (not visible in this view) and a discharge at the left. Sketch the EFD for this device.

110 VAC

discharge

hidden inlet

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Example

Big-box retailers have warming units near their entrance doors. They keep greeters warm, help customers acclimate to the change in temperature between inside and out, and help reduce energy costs. One such unit is shown below.

The left view shows the heated air vent while the right view shows the natural gas line to feed the heater, the vent pipe for burned exhaust gases, and the fan that moves cool air into the heater thereby forcing warmer air out. Sketch the corresponding EFD.