The measurement of temperature of a gas stream.

Question

A spherical thermocouple junction of diameter 0.706mm is to be used for the measurement of temperature of a gas stream. The convective heat transfer coefficient on the bead surface is 400W/m²K. Thermo-physical properties of thermocouple material are k = 20W/mK, C = 400J/kgK and r = 8500 kg/m³. If the thermocouple initially at 30⁰C is placed in a hot stream of 300⁰C, the time taken by the bead to reach 298⁰C is                                                                                            

      (a) 2.35s                                                             (b) 4.9s

      (c) 14.7s                                                             (d) 29.4s