A hot water heating coil has a set-point of 35°C with a throttling range of 10°C. The heat output of the coil varies from 0 kW to 50 kW. Assuming that a proportional controller is used to maintain the air temperature set-point, determine the proportional gain for the controller and the relationship between the output air temperature and the heat rate provided by the coil. Assume steady-state operation.