Question

$\huge \mathfrak \pink{question}$

At 30°C the area of sheet of Aluminium is 40 cm² and coefficient of linear expansion is 24×10⁶/°C. Determine the final temperature if the final area is 40.2 cm² ?

​

Answer 1

$\huge \mathtt \pink{ \underline {\underline{Answer : }}}$

$\mathtt {\underline{Given : }}$

The initial temperature (T1) = 30°C

The coefficient of linear expansion (α) = 24 x 10 - 6°C - 1

The coefficient of area expansion (β) = 2a = 2 x 24 x 10 - 6°C - 1 = 48 x 10-6°C - 1

The initial area (A1) = 40 cm2

The final area (A2) = 40.2 cm2

The change in area (ΔA) = 40.2 cm2 – 40 cm2 = 0.2 cm2

$\mathtt { \underline{To \: Find :}}$

The final temperature (T2) = ?

$\mathtt{ \underline{Solution :}}$

Formula of the change in area (ΔA) :

ΔA = β A1 ΔT

The final temperature (T2) :

ΔA = β A1 (T2 – T1)

0.2 cm2 = (48 x 10-6°C -1)(40 cm2)(T2 – 30°C)

0.2 = (1920 x 10-6)(T2 – 30)

0.2 = (1.920 x 10-3)(T2 – 30)

0.2 = (2 x 10-3)(T2 – 30)

0.2 / (2 x 10-3) = T2 – 30

0.1 x 103 = T2 – 30

1 x 102 = T2 – 30

100 = T2 – 30

100 + 30 = T2

T2 = 130°C

The final temperature is 130°C.

________________________________

Answer 2

$\huge \mathtt \pink{ \underline {\underline{Answer : }}}$

$\mathtt {\underline{Given : }}$

The initial temperature (T1) = 30°C

The coefficient of linear expansion (α) = 24 x 10 - 6°C - 1

The coefficient of area expansion (β) = 2a = 2 x 24 x 10 - 6°C - 1 = 48 x 10-6°C - 1

The initial area (A1) = 40 cm2

The final area (A2) = 40.2 cm2

The change in area (ΔA) = 40.2 cm2 – 40 cm2 = 0.2 cm2

$\mathtt { \underline{To \: Find :}}$

The final temperature (T2) = ?

$\mathtt{ \underline{Solution :}}$

Formula of the change in area (ΔA) :

ΔA = β A1 ΔT

The final temperature (T2) :

ΔA = β A1 (T2 – T1)

0.2 cm2 = (48 x 10-6°C -1)(40 cm2)(T2 – 30°C)

0.2 = (1920 x 10-6)(T2 – 30)

0.2 = (1.920 x 10-3)(T2 – 30)

0.2 = (2 x 10-3)(T2 – 30)

0.2 / (2 x 10-3) = T2 – 30

0.1 x 103 = T2 – 30

1 x 102 = T2 – 30

100 = T2 – 30

100 + 30 = T2

T2 = 130°C

The final temperature is 130°C.

________________________________