THERMODYNAMICS I: BASICS, ENERGY, & THERMAL EFFICIENCY

Introduction:

 There are seven basic properties to describe a state: enthalpy, entropy, internal energy, temperature, pressure, density, and specific volume. If two are known, the others can be calculated.  Intensive properties are independent of amount of mass, denoted with lowercase  Extensive properties are dependent on the amount of mass, denoted with uppercase.  The four tools used in introductory thermodynamics are the 1st and 2nd laws of thermodynamics, conservation of mass, and equations of state.  Temperature scale conversions are as follows:

5 T(℃) = ( ) ∗ [푇(℃) − 32] 9 푇(퐾) = 푇(℃) + 273.15

푇(°푅) = 푇(℉) + 459.12

Energy:

 There are 5 forms of energy: kinetic (퐾퐸), potential (푃퐸), internal (푈), work (푊), and heat (푄)  A change in energy of a system occurs through work done or heat transferred  Energy sign convention:

> 0 positive Work done by the system W < 0 negative Work done on the system > 0 positive Heat transferred into system Q < 0 negative Heat transferred out of system

 Energy balance equation:

∆퐸 = 퐸2 − 퐸1 = ∆푈 + ∆퐾퐸 + ∆푃퐸 = (푄푖푛 + 푊푖푛 − 푄표푢푡 − 푊표푢푡) + ∆퐾퐸 + ∆푃퐸

Rates of Change:

The energy balance equation also applied to rates of change of energy, with a superscript dot centered over a letter signifying the derivative with respect to time:

푑퐸 퐸̇ = 푑푡

The subscript “cv” is used to notate the system is a control volume (∆푉 = 0).

 Mass balance: 푑푚 푐푣 = ∑ 푚̇ − ∑ 푚̇ 푑푡 푖푛 푒푥푖푡 푖푛 푒푥푖푡

 Energy balance: 푑퐸 V2 푣2 푐푣 = 퐸̇ − 퐸̇ = 푄̇ − 푊̇ + 푚̇ (ℎ + 푖푛 + 𝑔푧 ) − 푚̇ (ℎ + 표푢푡 + 𝑔푧 ) 푑푡 푖푛 표푢푡 푖푛 푖푛 2 푖푛 표푢푡 표푢푡 2 표푢푡

Based on the assumptions of a given problem, many terms will cancel out to simplify the 푣2 푣2 equation. For example, 푖푛 − 표푢푡 and 𝑔푧 − 𝑔푧 = 0 when changes kinetic and potential energy 2 2 푖푛 표푢푡 are assumed to be zero. It is good practice to start every relevant problem with the entire equation before cancelling out any terms. Thermal Efficiency:

The following table notes three types of thermal processes and their respective thermal efficiencies. Carnot refers to a perfectly reversible processes, such that ∆푠 = 0

Type C.O.P General Expansion Carnot Equivalent

푤푐푦푐푙푒 푄표푢푡 푇퐶 Power Cycle 휂 = = 1 − 1 − 푄푖푛 푄푖푛 푇퐻

푄푖푛 푄푖푛 푇퐶 Refrigeration 훽 = = 푊푐푦푐푙푒 푄표푢푡 − 푄푖푛 푇퐻 − 푇퐶

푄표푢푡 푄표푢푡 푇퐻 Heat Pump 훾 = = 푊푐푦푐푙푒 (푄표푢푡 − 푄푖푛) 푇퐻 − 푇퐶

For more information, visit a tutor. All appointments are available in-person at the Student Success Center, located in the Library, or online. Adapted from Moran, M. J., Shapiro, H. N., Boettner, D. D., & Bailey, M. B. (2014). Fundamentals of Engineering Thermodynamics. Hoboken, NJ: Wiley.