Consider a unit mass of \(\mathrm{N}_{2}\) in equilibrium at \(p=1 \mathrm{~atm}\) and \(T=300 \mathrm{~K}\). For these conditions, the vibrational relaxation time is \(190 \mathrm{~s}\). Assume that, by some mechanism, the vibrational energy is instantaneously increased by a factor of 100, with all other properties remaining unchanged. At the end of \(1 \mathrm{~min}\) after excitation, what is the value of the vibrational energy relative to the equilibrium value? Assume that \(p\) and \(T\) remain constant at \(1 \mathrm{~atm}\) and \(300 \mathrm{~K}\), respectively.