In an experiment performed with a mercury thermometer, the following results were obtained when the ambient temperature was $80C$ and the steady$-$state temperature of the thermometer was $25C.$ The thermometer has a mass of $2g,$ a specific heat of $30\frac{J}{g}C$ and a surface area of $2c{m}^2.$

$\backslash$table$[[t(s),2,4,6,8,10],[T(C),36,45,52,58,63]]$

In the light of this information, indicate whether the following statements are true $($F$)$ or false $($F$).$ If the statement is wrong, write the correct answer. State every action you take clearly and concisely.

a$.$ The average time constant of the thermometer is $7\mathrm{.}23s.()$

b$.$ At $t=15s,$ the steady$-$state temperature of the thermometer is $36C.()$

c$.$ The transfer function of the mercury thermometer $\frac{?}{Txs+1}$ expressed as $G(s)=1.()$

D$.$ The temperature that the thermometer will show after $30s$ is $69C.()$

to$.$ The temperature that the thermometer will show after $30s$ depends on the environmental ternperature, the steady$-$state temperature of the thermometer and the time constant. $()$

f$.$ The new steady$-$state temperature that the thermometer will reach after waiting a sufficient amount of time It is $105C.()$

g$.$ The convection film coefficient of the system is $11\mathrm{.}15\frac{W}{c}{m}^{20}C.()$

h$.$ The steady state of the thermometer was disturbed by a shock function of $25C.()$