A nozzle, to which steam at \(500 \mathrm{kPa}\) and \(623 \mathrm{~K}\) is entering at the rate of \(12 \mathrm{~kg} / \mathrm{s}\) and leaving at \(500 \mathrm{kPa}\) and \(523 \mathrm{~K}\), is fitted to a long pipe. The amount of heat loss to the environment is calculated to be \(120 \mathrm{~kW}\). If the velocity of steam at the entrance of the nozzle is assumed to be negligible, then find the velocity at the outlet. We are given that the enthalpy of steam at \(500 \mathrm{kPa}\) and \(623 \mathrm{~K}\) is \(3168 \mathrm{~kJ} / \mathrm{kg}\) and the enthalpy of steam at \(50 \mathrm{kPa}\) and \(523 \mathrm{~K}\) is \(2976 \mathrm{~kJ} / \mathrm{kg}\).