A monatomic ideal gas is contained adiabatically at a temperature of $300K$ and a pressure of $40$atm. The gas is contained adiabatically in a vessel with $5$ moles. The gas expands irreversibly, and the pressure suddenly drops to $10$atm. The irreversible expansion produced $3500J$ of work. Calculate the final temperature of the gas after the irreversible expansion. Compare temperature with that if the gas would expand reversibly from $40$ to $10$atm. Calculate the change of entropy due to the irreversible expansion using two different reversible routes.