Zeroth and First Laws
The zeroth law establishes thermal equilibrium and temperature measurement. The first law is conservation of energy:
- Zeroth law: if A is in thermal equilibrium with C, and B is in equilibrium with C, then A and B are in equilibrium
- Closed system first law: Q - W = delta_U
- Q = heat added to system (positive in), W = work done by system (positive out)
- Open system (steady-flow): Q - W = m_dot * [delta_h + delta_KE + delta_PE]
- Enthalpy: h = u + Pv (internal energy plus flow work)
Second Law of Thermodynamics
The second law introduces the concept of entropy and limits the efficiency of processes:
- Clausius statement: heat cannot flow from cold to hot without external work
- Kelvin-Planck: no cyclic device can convert heat entirely to work
- Entropy: delta_S = integral of (delta_Q_rev / T)
- For an irreversible process: delta_S > integral of (delta_Q / T)
- Entropy of the universe always increases for real processes
- Isentropic process: constant entropy (reversible and adiabatic)
Ideal Gas Relations
- PV = nRT or Pv = RT (specific volume form)
- For air: R = 287 J/(kg*K), c_p = 1.005 kJ/(kg*K), c_v = 0.718 kJ/(kg*K), k = 1.4
- Relationship: c_p - c_v = R and k = c_p/c_v
- Isentropic relations: T2/T1 = (P2/P1)^((k-1)/k) = (V1/V2)^(k-1)
Power Cycles
- Carnot cycle: maximum theoretical efficiency, eta = 1 - T_L/T_H
- Otto cycle (spark ignition): constant volume heat addition, eta = 1 - 1/r^(k-1)
- Diesel cycle: constant pressure heat addition
- Rankine cycle (steam power): pump, boiler, turbine, condenser
- Brayton cycle (gas turbine): compressor, combustor, turbine
- Improvements: reheat, regeneration, intercooling increase cycle efficiency
Refrigeration Cycles
- Vapor compression: compressor, condenser, expansion valve, evaporator
- COP_refrigerator = Q_L / W_net (cooling capacity per unit work)
- COP_heat_pump = Q_H / W_net (heating capacity per unit work)
- Carnot COP_ref = T_L / (T_H - T_L)
- Carnot COP_hp = T_H / (T_H - T_L)
Psychrometrics
- Dry-bulb temperature: ordinary temperature measured by a thermometer
- Wet-bulb temperature: temperature measured with a wetted wick (evaporative cooling)
- Dew point: temperature at which moisture begins to condense
- Relative humidity: phi = P_v / P_sat (actual vapor pressure / saturation pressure)
- Humidity ratio: omega = 0.622 * P_v / (P_atm - P_v)
- Psychrometric chart: graphical tool for determining moist air properties