Two samples of gas initially at the same temperature and pressure are compressed from volume V to V/2 One - Physics - Thermodynamics

Question

Two samples of gas initially at the same temperature and pressure
are compressed from volume V to V/2 One sample is compressed
isothermally and the other adiabatically in which case the pressure
will be higher ?

Plzzz explain experts

Jyoti Pant · Accepted Answer

Suppose,Final pressure during adiabatic compression=PaFinal pressure during isothermal compression=PiFor isothermal compression,PV=Pi(V2)Or Pi=2P----(i)For adiabatic compression,PVγ=Pa(V2)γOr Pa=2γP---(ii)Dividing (ii) by (i),PaPi=2γP2P=2γ2Since γ>1, so 2γ2>1Therefore, PaPi>1Or Pa> PiThus, final pressure during adiabatic compression is greater than the pressure during isothermal compression

Two samples of gas initially at the same temperature and pressure are compressed from volume V to V/2 .One sample is compressed isothermally and the other adiabatically .in which case the pressure will be higher ? Plzzz explain experts

Two samples of gas initially at the same temperature and pressure are compressed from volume V to V/2 .One sample is compressed isothermally and the other adiabatically .in which case the pressure will be higher ?

Plzzz explain experts