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? [Mothers Global 2024]
Doubt by Raghav
Solution :
Here
Initial Volume of the gas (V1) = V
Final Volume of the gas (V2) = V/2
Initial Volume of the gas (V1) = V
Final Volume of the gas (V2) = V/2
Let
Initial Pressure of the gas = P1
Initial Pressure of the gas = P1
Final Pressure of the gas = P2
During Isothermal Compression
PV = Constant
P1V1=P2V2
P1(V)=P2(V/2)
P1=P2/2
2P1=P2
P2=2P1 — (1)
PV = Constant
P1V1=P2V2
P1(V)=P2(V/2)
P1=P2/2
2P1=P2
P2=2P1 — (1)
During Adiabatic Compression
PVγ = constant
P1V1γ=P2V2γ
P1(V)γ=P2(V/2)γ
P1=P2/2γ
2γP1=P2
P2=2γP1 — (2)
Here γ=Cp/Cv which is always greater than 1.
The final pressure in the case of Adiabatic compression is greater than in the case of Isothermal compression.
P1V1γ=P2V2γ
P1(V)γ=P2(V/2)γ
P1=P2/2γ
2γP1=P2
P2=2γP1 — (2)
Here γ=Cp/Cv which is always greater than 1.
The final pressure in the case of Adiabatic compression is greater than in the case of Isothermal compression.