Unsteady state heat conduction 2

A thermocouple junction of spherical form is to be used to measured the temperature of a gas stream. Take h = 400 w/m2-k, K = 20 w/m-k, Cp = 400 J/kg-k, ρ = 8484 kg/m3. Find the diameter of thermocouple to have a time constant (τ) of 1 second
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In the above case, If the junction temperature is 27° C initially. Then it is placed in gas stream of 200° C. Find at what time thermocouple will show temperature of 198° C
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