The First Law of Thermodynamics (Physics)

Recall cards on the first law of thermodynamics. Thermodynamic systems: system, boundary, and surroundings; open, closed, and isolated systems; thermal equilibrium and the zeroth law; equations of state f(p, V, T) = 0 and pV - nRT = 0; extensive versus intensive variables; and pV diagrams. Work, heat, and internal energy: dW = p dV, W as the integral of p dV and the area under a pV curve, the sign of work in expansion and compression, the path dependence of work, and the work in isothermal (nRT ln(V2/V1)), isobaric (p(V2 - V1)), and isochoric (zero) processes; internal energy as the total molecular energy, E_int = (3/2) nRT for a monatomic ideal gas, and the quasi-static process. The first law itself: Delta E_int = Q - W, the sign conventions for Q and W, the differential form dE_int = dQ - dW, internal energy as a path-independent state function, and the isothermal, cyclic, and isolated-system cases. Thermodynamic processes: isothermal, adiabatic, isobaric, isochoric, cyclic, and non-quasi-static, with Q = W for a cycle. Heat capacities of an ideal gas: C_V and C_p, Q = n C_V Delta T and Q = n C_p Delta T, dE_int = n C_V dT, Mayer's relation C_p = C_V + R, the monatomic, diatomic, and polyatomic values, and C_V = (d/2) R. Adiabatic processes: Q = 0, Delta E_int = -W, pV^gamma = constant, TV^(gamma-1) = constant, the adiabatic index gamma = C_p/C_V > 1, the steeper adiabatic slope, free expansion at constant temperature, and engine knocking.