pv = p1v1.
Work done during expansion per pound of air
_ _
/v2 /v2
= | p dv = p1v1 | dv/v
_/v1 _/v1
= p1v1 log_[epsilon] v2v1 = p1v1 log_[epsilon] p1p2. (1)
Since the weight per cubic foot is the reciprocal of the volume per
pound, this may be written
(p1/G1) log_[epsilon] G1/G2. (1a)
Then the expansion curve ab is a common hyperbola.
_Case 2._--No heat is supplied to the air during expansion. Then the
air loses an amount of heat equivalent to the external work done and
the temperature falls. Adiabatic expansion.