Thermodynamics - Quick Revision
Basic ideas
- Thermodynamic system + surroundings; state variables P, V, T, U (internal energy is a state function; heat Q and work W are path functions).
- Zeroth law: if A and B are each in thermal equilibrium with C, they are in equilibrium with each other -> defines temperature.
First law
- dQ = dU + dW (heat added = rise in internal energy + work done by gas), dW = P dV.
- For an ideal gas U depends only on T.
Processes
- Isothermal (T const): dU = 0, W = nRT ln(V2/V1).
- Adiabatic (Q = 0): PV^gamma = const, TV^(g-1) = const, W = nR(T1-T2)/(gamma-1).
- Isobaric (P const): W = P dV; Isochoric (V const): W = 0, dQ = dU.
- Cp - Cv = R, gamma = Cp/Cv = 1 + 2/f.
Second law and engines
- Second law: heat cannot flow spontaneously cold->hot (Clausius); no engine can convert all heat to work (Kelvin-Planck).
- Heat engine efficiency eta = W/Q1 = 1 - Q2/Q1.
- Carnot engine (reversible) is the most efficient: eta = 1 - T2/T1; no real engine between the same two temperatures can beat it.
- Refrigerator/heat pump: COP = Q2/W = T2/(T1 - T2).