Thermodynamics Fundamentals for the FE Exam
Thermodynamics is a core topic on the FE Mechanical and FE Chemical exams, and it appears on other disciplines as well. The subject deals with energy, its transformations, and the relationship between heat, work, and the properties of matter. Understanding the two fundamental laws is the key to solving thermodynamics problems.
Basic Concepts and Definitions
- System: The region of space or matter being studied. It can be open (mass crosses the boundary), closed (no mass crosses), or isolated (no mass or energy crosses).
- Surroundings: Everything outside the system.
- State: Defined by the values of properties (pressure, temperature, volume, etc.).
- Process: A change from one state to another.
- Property: A measurable characteristic of the system (intensive: independent of mass, like T and P; extensive: depends on mass, like V and U).
The First Law of Thermodynamics
The first law is the conservation of energy principle applied to thermodynamic systems.
For a Closed System
Q - W = delta_U
Where Q is heat added to the system, W is work done by the system, and delta_U is the change in internal energy. Sign convention matters: heat added to the system and work done by the system are positive.
For an Open System (Steady-State)
Q_dot - W_dot = m_dot * (h_2 - h_1 + (V_2^2 - V_1^2)/2 + g*(z_2 - z_1))
Where h is specific enthalpy, V is velocity, z is elevation, and m_dot is mass flow rate. For many problems, kinetic and potential energy changes are negligible.
Important Processes
- Isothermal: Constant temperature. For an ideal gas: W = nRT * ln(V_2/V_1).
- Isobaric: Constant pressure. W = P * (V_2 - V_1). Q = m * c_p * delta_T.
- Isochoric (Isometric): Constant volume. W = 0. Q = m * c_v * delta_T.
- Adiabatic: No heat transfer (Q = 0). For a reversible adiabatic process of an ideal gas: P*V^gamma = constant, T*V^(gamma-1) = constant.
- Polytropic: P*V^n = constant, where n is the polytropic exponent.
Ideal Gas Law
PV = nRT (or PV = mRT, where R is the specific gas constant)
The ideal gas law is valid for gases at moderate temperatures and low pressures (far from condensation). It is used extensively in thermodynamics problems on the FE exam.
The Second Law of Thermodynamics
The second law establishes the direction of natural processes and introduces entropy.
Entropy
Entropy (S) is a measure of the disorder or randomness of a system. The second law states that the entropy of an isolated system never decreases. For a reversible process: dS = delta_Q / T. For an irreversible process: dS is greater than delta_Q / T.
Key Second Law Statements
- Kelvin-Planck statement: It is impossible to construct a heat engine that produces net work in a complete cycle while exchanging heat with only a single reservoir.
- Clausius statement: It is impossible to construct a device that transfers heat from a cold body to a hot body without any external work input.
Heat Engines
A heat engine converts heat into work. It operates between a hot reservoir (T_H) and a cold reservoir (T_C):
- Thermal efficiency: eta = W_net / Q_H = 1 - Q_C / Q_H
- Carnot efficiency (maximum possible): eta_Carnot = 1 - T_C / T_H (temperatures in absolute units)
Refrigerators and Heat Pumps
- Refrigerator COP: COP_R = Q_C / W_net = Q_C / (Q_H - Q_C)
- Heat pump COP: COP_HP = Q_H / W_net = Q_H / (Q_H - Q_C)
- Carnot COP (refrigerator): COP_R = T_C / (T_H - T_C)
- Carnot COP (heat pump): COP_HP = T_H / (T_H - T_C)
Property Tables and Diagrams
For real substances (water, refrigerants), properties are found from tables or diagrams:
- Steam tables: Give properties of water and steam at various pressures and temperatures. Include saturated liquid, saturated vapor, and superheated vapor data.
- Quality (x): For a liquid-vapor mixture, x = mass of vapor / total mass. Properties: h = h_f + x * h_fg, s = s_f + x * s_fg.
- T-s diagram: Temperature vs. entropy. Useful for visualizing cycles and processes.
- P-v diagram: Pressure vs. specific volume. Shows phase boundaries and process paths.
Common FE Exam Problem Types
- Applying the first law to closed or open systems
- Calculating work for various processes (isothermal, isobaric, adiabatic)
- Finding thermal efficiency or COP
- Using steam tables to find properties at given conditions
- Determining the direction of heat transfer
- Analyzing Carnot cycle efficiency
Thermodynamics on the FE exam rewards understanding over memorization. Know the first and second laws, understand the different process types, and practice using the property tables in the reference handbook.