A thermocouple whose surface is diffuse and gray with an

emissivity of $0\mathrm{.}60$ indicates a temperature of $165\mathrm{.}0$C when used

to measure the temperature of a gas flowing at low speed through

a large duct. The walls of the duct have an emissivity of $0\mathrm{.}85$

and are at a uniform temperature of $450\mathrm{.}0$C$.$ If the convection

coefficient for the gas flowing over the thermocouple is $75\mathrm{.}0$

W$/($m$2-$K$)$ and there are negligible conduction losses from the

thermocouple, calculate the actual temperature of the gas.