Question
Question: An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adi...
An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume (g = 1.4 and 2–1.4 = 0.38). The ratio of the final to initial pressure is
A
0.76 : 1
B
1 : 1
C
0.66 : 1
D
0.86 : 1
Answer
0.76 : 1
Explanation
Solution
Let V be the original volume of the gas. For a isothermal process PV = constant
∴PiTi=PfVf
Vf=Vi(PfPi)=V(Pi2Pi()2V)
For an adiabatic process
PVγ= Constant
According to questions
∴(2Pi)(2V)γ=PfVγ
PiPf=2(2)−γ=2(2)−1,4=2(0.38)=10.76