$(8)$ A thermometer placed in a well filled with oil is required to measure the temperature of gas flowing

in a pipe. The well is $140$ mm long and is made of steel $(k=58\frac{W}{m}-K,$ and $1$ mm thick. The temperature

recorded by the thermometer is $100C$ while the pipe wall is at $50C.$ The surface heat transfer coefficient

from air to the well is $29\frac{W}{m^2}K.$

Estimate the true temperature of the air and the percentage error.

In what way the thermometric error can be reduced?

$[$Ans: $104\mathrm{.}5C]$