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Two samples, A and B of a gas at the sam...

Two samples, A and B of a gas at the same initial temperature and pressure are compressed from volume V to V/2, A isothermally and B adiabatically. The final pressure of A will be

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Let `" "` Intial volume , `V_(1) = V` and pressure . `P_(1) = P , `
final volume, `V_(2)= (V)/(2)` and final pressure , `P_(2) = ?`
For isothermal compression `P_(2)V_(2) = P_(1)V_(1)` or `P_(2) = (P_(1)V_(1))/(V_(2)) = (PV)/(V/2) = 2P`
For adiabatic compression `P_(2)' = P_(1)[(V_(1))/(V_(2))]^(gamma) implies P_(2)' = P[(V)/(V//2)]^(gamma) = 2^(gamma) P implies P_(2)' = 2^(gamma) P gammagt1`
`therefore " " 2^(gamma) gt2` and `P_(2)'gtP_(2)`
Pressure during adiabatic compression is greater than the pressure during isothermal compression.
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