Chapter 4, Problem 28P

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 percent of the initial temperature difference must be within 5 s. The properties of the thermocouple junction are $k=35\text{ W/m}\text{.K, }p=8500{\text{ kg/m}}^{\text{3}},andcp=320\text{ J/kg}\text{.K}$. If the heat transfer coefficient between the thermocouple junction and the gas is 250 W/m² K, determine the diameter of the junction.