This question considers a thermocouple. It's properties are:

Diameter: $0\mathrm{.}8$ mm

Thermal Conductivity, $k$:$20\frac{W}{m}K$

Specific heat capacity: $400\frac{J}{k}gK$

Density: $8500$ kg$/$m$^3$

If the thermocouple is at $22C,$ how long does it take $($in s$)$ to reach $223C$ in a gas flow at $224C$ with a convective heat transfer coefficient of $300\frac{W}{m^2}K?$