Chapter 8 - Modes of Work and Conjugate Variables

what is the equation for internal energy in stretching a rubber band

dU = d(dash)Q + tension dx

why is the tension dx positive

is we extend band to tension + dtension then work done by the system is dW = - tension dx

how can we generalise dU = dQ - dW

let -P be a generalised force and dV be generalised displacement and PdV have the unites of energy

what is the conjugate variable in general form of the first law

(P,V) or (tension, x) and generally ( xi, Xi)

what are the extensive and intensive variables in the general form of the first law

P,tension and xi are intensive and v,x and Xi are extensive

what is the general form of the first law

with generalised forces xi driving generalised displacements Xi, dU = d(dash)Q + sum from i=1 to m of xidXi