Question

2 mols of a gas (gamma = 1.4) undergo an adiabatic expansion. If the gas volume changed from 2L to 4L, and the initial temperature, what is the final temperature and pressure if the initial temperature was 300 K?

Answer 1

n= no. of moles = 2

Initial volume = Vi = 2 L = 0.002 m3

Final volume = Vf = 4L = 0.004 m3

Initial Temperature = Ti = 300 K

Using Ideal gas equation, the initial pressure Pi = nRTi / Vi = 2*8.314*300/ 0.002 = 2494200 Pa = 2.494*106 Pa

gamma =

As per Adiabatic expansion, is constant.

Hence

= 0.945*106 Pa = Final Pressure.

Final Temperature = Tf = PfVf/ nR = 0.945*106*0.004/(2*8.314) = 227.32 K