Initial pressure of the gas, P1 = 100 kPa
Initial volume of the gas,V1 = 400 cm3
= 400 × 10−6 m3
Initial temperature of the gas, T1 = 300 K
(a) The gas is suddenly compressed to volume, V2 = 100 cm3 .
So, this is an adiabatic process.
For an adiabatic process,
P1V1γ = P2V2γ
⇒ 105 × (400)1.5 = P2 (100)1.5
⇒ P2 = 105(4)1.5 = 800 kPa
Also,
T1Vγ−1 = T2V2γ−1
⇒ 300 × (400)1.5−1 = T2 (100)1.5−1
⇒ 300 × (400)0.5 = T2 (100)0.5
⇒ T2 = 600 K
(b) If the container is slowly compressed, the heat transfer is zero, even thought the walls are adiabatic.
Thus, the values remain same. Thus,
P2 = 800 kPa
T2 = 600 K