Ideal Gas Law
- PV = nRT (n = moles, R = 8.314 J/(mol*K))
- PV = mRT (m = mass, R = specific gas constant)
- R_specific = R_universal / M (M = molar mass)
- For air: R = 287 J/(kg*K) or 53.35 ft*lbf/(lbm*R)
First Law of Thermodynamics
- Closed system: Q - W = delta_U (heat minus work equals change in internal energy)
- Open system (SFEE): Q - W = m_dot * (delta_h + delta_KE + delta_PE)
- Sign convention: Q positive into system, W positive out of system
- For ideal gas: delta_U = m * c_v * delta_T
- For ideal gas: delta_H = m * c_p * delta_T
Second Law of Thermodynamics
- Clausius: heat flows spontaneously only from hot to cold
- Kelvin-Planck: no heat engine can convert 100% of heat to work
- Entropy change: delta_S >= Q/T (equality for reversible processes)
- For ideal gas: delta_s = c_p * ln(T2/T1) - R * ln(P2/P1)
- For ideal gas: delta_s = c_v * ln(T2/T1) + R * ln(V2/V1)
Carnot Cycle
- Maximum efficiency for a heat engine between two temperatures
- eta_Carnot = 1 - T_L/T_H (temperatures must be in absolute units, K or R)
- COP_refrigerator = T_L / (T_H - T_L)
- COP_heat_pump = T_H / (T_H - T_L)
- Consists of: two isothermal + two isentropic (adiabatic reversible) processes
Process Types
- Isothermal: constant temperature (PV = constant for ideal gas)
- Isobaric: constant pressure (W = P * delta_V)
- Isochoric (isometric): constant volume (W = 0)
- Isentropic: constant entropy (PV^k = constant, where k = c_p/c_v)
- Polytropic: PV^n = constant (general case)
- Adiabatic: no heat transfer (Q = 0)
Heat Engine and Refrigeration Cycles
- Heat engine efficiency: eta = W_net / Q_H = 1 - Q_L/Q_H
- Otto cycle (gasoline engine): eta = 1 - 1/r^(k-1) (r = compression ratio)
- Diesel cycle: eta = 1 - (1/r^(k-1)) * [(r_c^k - 1) / (k*(r_c - 1))]
- Rankine cycle: basic steam power cycle (pump, boiler, turbine, condenser)
- Vapor compression refrigeration: compressor, condenser, expansion valve, evaporator