A gas has an initial volume of 1L at a pressure of 8 atm. An adiabatic expansion takes the gas to a pressure of 1 atm. What will be its final volume? Given , `gamm = 1.5`.

Explanation

`p_(1)V_(1)^(gamma) = p_(2)V_(2)^(gamma) = V_(1)^(gamma) cdot (p_1)/(p_2)`
Here, `p_(1) = 8 atm, V_(1) = 1 l, p_(2) = 1 atm`
`:. V_(2) = V_(1) ((p_1)/(p_2))^(1/gamma) = 1 xx (8/1)^(2/3) [ gamma = 1.5 = 3/2 , 1/(gamma) = 2/3]`
`= (2^3)^(2/3) = 2^(2) = 4L`.