System - a selected region of space, matter, or objects to which we apply the laws of thermodynamics.
Energy, E - Capacity to store or cause work, heat (J, BTU, calorie, kcal, kW-hr)) (E = KE + PE + U)
- KE = 1/2mV2
- PE = mg(Z-Zref)
- Internal energy, U - a collection (sum) of microscopic modes including molecular translation, rotation (types of microscopic kinetic energy) and vibration, plus energy related to intermolecular
forces, energy associated with atomic bonding (both are types of microscopic potential energy)
Intermolecular Potential Energy, Uintermolecular
ℇ - “well depth” (units of energy); σ - “collision diameter”; Rmin - “separation at minimum energy” (for two molecules of methane), dU = Fdr
Work, W - the organized “flow” or “transfer” of energy (J, kW-hr))
- W = F*d = PΔV = ∫PdV = T*θ (for shaft) = ΔV*I*time (for elec)
Heat, Q - the disorganized “flow” or “transfer” of energy (J, BTU, calorie, kcal)
Power, W’ - rate of doing work (Watt, horsepower)
Rate of heat flow , Q’ (W, BTU/hr, cal/min)
First law for a closed system: ΔE = Q - W → dE/dt = Q’ - W’
- Q is heat addition, + as input, - as output
- W is work out, + as output, - as input
Adiabatic means no Q (no heat loss)
Steady state means no dE/dt (no change in energy), all time derivatives set to 0, any heat or mass flow is constant
Isolated system - no interactions with surroundings at all (no Q, W, mass entry/exit)
“Well insulated” - negligible heat transfer across insulated zone (no Q)
ΔU = mCΔT (assume water only, no vessel walls or evaporation); dU/dt = mCdT/dt
W = W’ * t
H = U + PV (directly related to heat effects with a constant P process with no work except expansion/contraction) →
PV diagram PT diagram
Incompressible substance model (approximate most liquids and solids)
- States V (specific volume) is nearly constant with changing P. U is function of T but not P
- U is a function of T, so its derivative Cv is also a function of T → Cv = Cp = C
Ideal gas model
- U is not a function of P or V (only T is needed to specify U)
- Use PV = nRT of PV = RT (V = specific volume V/n)
- Cv = dU/dT; Cp = dH/dT; Cp = Cv + R (only for ideal gases) → ΔU = ∫CvdT; ΔH = ∫CpdT
- For monoatomic ideal gases, Cv = 3/2R; Cp = 5/2R
- PV = zRT (compressibility factor Z; estimate with graph from Tr=T/Tcr and Pr=P/Pcr)
- Adiabatic lapse rate dT/dz
Vapor/liquid systems
- If saturated, only need on property to define state
- Superheated = not saturated (heated beyond sat state)
- If two-phase mixture:
First law of open systems:
dE/dt = Q’ - W’ + m’[Hin-Hout]
Common flow devices
For heat exchanger, transfer heat from one fluid to another without mixing, no work, g or l, fluid can be external, pressure is often nearly constant, named condenser, boiler, chiller, evaporator, pre-heater, cooling
coil, and radiator
**The Psat value for a liquid { Psat = f(T only) } is also referred to as its “vapor pressure” The vapor pressure can be thought of as a liquid property – the pressure the molecules exert as they randomly try to
leave the liquid phase
