posted by joanna .
an ideal monatomic gas is allow to expand slowly until its pressure is reduce to exactly half its original volume. By what factor those the volume change if the process is (1)isothermal (2) adiabatic
You must have meant "..until its pressure is reduce to exactly half its original VALUE". Pressure cannot equal volume. They have different dimensions.
(1) P*V = constant
V2/V1 = P1/P2 = 2
(2) P*V^5/3 = constant (for a monatomic gas)
(V2/V1)^(5/3) = P1/P2 = 2
V2/V1 = 2^(3/5) = 1.5157