a$.$ You are tasked with determining the diameter of a spherical thermocouple junctionrequired to achieve a thermal time constant of one second for measuring thetemperature of a gas stream. Relevant parameters include the heat transfer coefficientof $400$ W$/$m$^2\backslash$deg C$,$ thermal conductivity of the thermocouple junction of $20$ W$/$m$\backslash$deg C$,$ specificheat capacity of $400$ J$/$kg$\backslash$deg C$,$ and density of $8500$ kg$/$m$^3.$b$.$ You're also asked to calculate the time it takes for the thermocouple junction to reach$198\backslash$deg C when initially at $25\backslash$deg C and placed in a gas stream at $(=200+70)\backslash$deg C$.$a$.$ Sketch the schematic of the system with complete labeling.