Thermodynamic Properties, Energy Balances, and Ideal Gases

Boundary before formula

Thermodynamics problems are easiest when the boundary is chosen first. A closed system has no mass crossing the boundary, so the first law usually tracks heat, work, and change in internal energy. A control volume has mass flow, so enthalpy appears naturally because it includes internal energy plus flow work. Turbines, compressors, nozzles, pumps, throttling valves, heat exchangers, boilers, and condensers are control-volume devices.

For a closed stationary system, the simplified balance is often Q - W = Delta U, depending on the sign convention used by the handbook. For a steady-flow control volume, the balance relates heat transfer, shaft work, inlet and outlet enthalpies, kinetic energy, and potential energy. FE questions commonly state that kinetic and potential energy changes are negligible. Use that permission when given, but do not assume it for nozzles, diffusers, or high-speed jets.

Property state selection

Property lookup is a decision tree. Start with the known pressure and temperature. If temperature equals saturation temperature at that pressure, the state is saturated. If temperature is above saturation temperature for that pressure, it is superheated vapor. If temperature is below saturation temperature, it is compressed or subcooled liquid. If pressure and temperature are not enough, a property such as specific volume, enthalpy, entropy, or quality may locate the region.

Quality x is the vapor mass fraction in a saturated mixture. It is not a generic dryness score for every vapor. If a state is superheated, quality is undefined. If a state is compressed liquid, quality is also undefined. Many FE distractors assign quality outside the dome.

Enthalpy and device models

Steady devices have standard simplifications. A throttling valve is usually h1 = h2. An adiabatic turbine with negligible kinetic and potential changes has shaft output related to enthalpy drop. A compressor requires shaft input related to enthalpy rise. A nozzle converts enthalpy drop into kinetic energy. A heat exchanger may have two flowing streams with no shaft work and negligible heat loss to surroundings, so one stream's enthalpy decrease equals the other's enthalpy increase after mass flow rates are included.

Mass flow matters. A 20 kJ/kg enthalpy rise is not a power until multiplied by kg/s. Likewise, table values in kJ/kg should not be treated as total kJ unless mass is one kilogram.

Ideal gases

Use the ideal-gas model when the problem says ideal gas, when air is at ordinary mechanical-engineering conditions, or when the state is far from saturation and the approximation is appropriate. Use absolute pressure and absolute temperature. In SI, air commonly uses R = 0.287 kJ/(kg*K), with cp near 1.005 kJ/(kgK) and cv near 0.718 kJ/(kgK) over ordinary ranges.

For ideal gases, internal energy depends on temperature, and enthalpy also depends on temperature. Constant-pressure heating uses q = cp Delta T for simple air models; constant-volume heating uses q = cv Delta T. Isentropic ideal-gas formulas use ratios of absolute temperatures and pressures with k = cp/cv.

FE table strategy

Read the units and table headings before interpolating. Steam, refrigerants, air, and psychrometric tables have different variables. If your answer is impossible, such as negative absolute temperature, quality above one for a supposed mixture, or turbine work larger than ideal without explanation, the issue is usually state selection rather than arithmetic.