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.
In this case it can be shown that
pvγ = p1v1γ,
where γ is the ratio of the specific heats of air at constant pressure and volume. Its value for air is 1.408, and for dry steam 1.135.
Work done during expansion per pound of air.
= ∫v2v1 p dv = p1v1γ ∫v2v1 dv/vγ
| = −{p1v1γ / (γ − 1)} {1/v2γ−1 − 1/v1γ−1} = {p1v1γ / (γ − 1)} {1/v1γ−1 − 1/v2γ−1} = {p1v1 / (γ − 1)} {1 − (v1/v2) γ−1}. |
(2)
The value of p1v1 for any given temperature can be found from the data already given.