In an experiment, the temperature of a hot gas stream is to be measured by a thermocouple with a spherical junction. Due to the nature of this experiment, the response time of the thermocouple to register 99% of the initial temperature difference must be within 5s. The properties of the thermocouple jinction are k=35 w/m.k, p=8500 kg/m^3, and cp = 320 J/kg.k. If the heat transfer coefficient between the thermocouple junction and the gas is 250 w/m^2.K, determine the diameter of the junction.