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The pressure (10^(5) Nm ^(-2)) of air f...

The pressure `(10^(5) Nm ^(-2))` of air filled in a vessel is decreased adiabatically so as to increase its volume three times. Calculate the pressure of air. Given `gamma-`for air = 1.4

Text Solution

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Initial pressure `P = 1 xx 10^5N//m^2`,initial volume = V, final volume V = 3V, final pressure = P. (say).
For adiabatic expansion, we have
`PV^(gamma)= P.V^(gamma)`
Substituting values.
`(1xx 10^5) V^(gamma) = P.(3V)^gamma`
or `10^5 = P.(3)^(1.4) or P. = (10^5) (1//3)^(1.4)`
Taking log
`log P. = 5 log 10 + 1.4 (log 1 - log 3)`
`= 5(1) + 1.4(0-0.4771) = 5 - 0.66794 = 4.33206`
`:. P. = 2.148 xx 10^4 N//m^2`
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