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Question
The volume of an ideal gas (γ = 1.5) is changed adiabatically from 4.00 litres to 3.00 litres. Find the ratio of (a) the final pressure to the initial pressure and (b) the final temperature to the initial temperature.
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Solution
Given,
γ = 1.5
Since the process is adiabatic, PVγ = constant.
(a) P1V1γ = P2V2γ
Given, V1 = 4 L
V2 = 3 L
we need to find `"P"_2/"P" _1.`
`=> "P"_2/"P"_1 = ("V"_1/"V"_2)`
` => (4/3)^1.5 = 1.5396 = 1.54`
(b) Also, for an adiabatic process,
TVγ−1 = constant
T1V1γ−1 = T2V2γ−1
`=> "T"_2/ "T"_1 = ("V"_1/"V"_2)^ (gamma-1) =(4/3)^0.5 = 1.154`
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