Question

An ideal gas is inside a closed piston cylinder. Its temperature 20.5oC. We want to make the final pressure two times as big as the initial, and the maximum temperature we can achieve is 115.2oC. What should be the maximum ratio of the final over the initial volume of the gas to achieve a final pressure two times as big as the initial?

Answer 1

P V = n R T
n and R are constant
so
P1 V1 / T1 = P2 V2 / T2
T1 = 273 + 20.5 = 293.5
T2 max = 115.2 +273 = 388.2
P2 = 2 P1
so
P1 V1 / 293.5 = 2 P1 V2 / 388.2
V2/V1 = (388.2 / 293.5) / 2 = 0.661