A certain mass of nitrogen was compressed `eta = 5.0` times (in terms of volume), first adiabatically, and then isothermally. In both cases the initial state of the gas was the same. Find the ratio of the respective works expended in each compression.

Explanation

Let `(p_0,V_0,T_0)` be the initial state of the gas.
We know `A_("adia") = (-v R Delta T)/(gamma - 1)` (work done by the gas)
But from the equation `TV^(gamma - 1) `= constant, we get `Delta T = T_0 (eta^(gamma - 1) - 1)`
Thus `A_("adia") = (-vRT_0(eta^(gamma - 1) - ))/(gamma - 1)`
On the other hand, we know `A_(iso) = vRT_0 1 n((1)/(eta)) = -v R T_0 1n eta` (work done by the gas )
Thus `(A_(adia))/(A_(iso)) = (eta^(gamma - 1) - 1)/((gamma - 1)1 n eta) = (5^(0.4) -1)/(0.4 xx 1n 5) = 1.4`.