91影视

• i) Edge length of the brass cube$at20掳CisL=30cmor30脳{10}^{-2}m$ is
• ii) Initial temperature $=20掳C$
• iii) Final temperature$=75掳C$

The linear expansion of length is given by:

$鈭�L=L{伪}_b鈭�T$ 鈥︹�� (i)

The total surface area of cube is given by:

$A=6{\left(L\right)}^2$ 鈥︹��. (ii)

The brass cube has six faces so that it has six-time linear expansion. So, the change in area due to expansion using equation (ii) is given as:
$$\begin{gathered} 鈭�A=6(L+鈭�L)(L+鈭�L)-6L^2(Since,newexpandedlengthis(L+鈭�L) \\ =6{(L+鈭�L)}^2-6L^2 \\ =6(L^2+鈭�L^2+2L鈭�L)-6L^2 \end{gathered}$$

Since,$鈭�L$ is very small,localid="1661433128129" $鈭�L^2鈮�0$. Hence,

$鈭�A=12L鈭�L$

Therefore, the change in area is determined as:

localid="1661432593498" $$\begin{gathered} 鈭�A=12(L伪鈭�T) \\ =12L^2{伪}_b鈭�T \\ =12脳{(30脳{10}^{-2})}^2脳19脳{10}^{-6}脳(75-20) \end{gathered}$$

(Since the linear coefficient of expansion for brass is$a_b=19脳{10}^{-8}\frac{1}{掳C}$)

$$\begin{gathered} 鈭�A=12脳900脳{10}^{-4}脳19脳{10}^{-6}脳55 \\ =0.0011m^2 \\ =11c{m}^2 \end{gathered}$$

Hence, the increase in the total surface area of the cube is$11c{m}^2$.