I. For a gas enclosed in a cylinder with movable piston: Work = dW = Fdx = pAdx = p(Adx) = pdV

 A. Work = pdV

 B. Work depends on the process or path

II. Heat energy that goes into a system as it goes from one state(1) to another state(2) either goes into work energy or changing the internal energy of the system. This is a statement of conservation of energy. The change in internal energy when a system goes from one state to another doesn't depend on the process or path, while both the heat added (or removed) and the work done does.

Change in internal energy = heat - work

dEint = dQ - dW

dQ = dEint +dW

A. Sign conventions: Q(in) = (+); Q(out) = (-); Work done on system = (-); Work done by system = (+)

III. Apply the First Law to the following processes for an ideal monatomic gas:

Note: Equation of state is pV=nRT

A. Isothermal (dT=0)

B. Isobaric (dp=0)

C. Isochoric (dV=0)

D. Adiabatic (dQ=0)