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प्रश्न
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.
उत्तर
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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