temperature diameter

Question

6.3 A square metal plate with sides 3,5 m long is at a temperature of 31 °C. It has a hole of 920 mm in the centre. The linear coefficient of expansion of the metal is 14.5 x 10-6 1°C. Calculate the following: 6.3.1 The temperature of the metal plate if it is heated until the sides are 3,57 m long each 6.3.2 The diameter of the hole at the final temperature

Answer 1

(6.3.1)

The side of the metal plate is 3.5m at Temperature of 31°C

Linear coefficient of expansion of metals is 14.5 * 10^-6.

We know that

where dl = change in the length

= Initial Length

α = Linear Coefficient of expansion of metals.

= Initial Temperature.

= Final Temperature.

The side of the square metallic plate expands from 3.5m to 3.57m

The Initial Temperature = 31°C

(3.57 - 3.5) = 3.5 * 14.5 * 10^-6 * (t1 - 31)

0.07 = 5.075 * 10^-5 ( t1 - 31)

t1 = 1410.3°C.

Therefore the temperature at which the metal expands to 3.57m is 1410.3°C.

Answer 2

(6.3.2)

The metallic plate has a hole of diameter 920 mm.

Then radius of the circle is 0.46m

Then area of the circle is given as π r².

Then diameter of the cicle is 2*0.4645 = 0.9290.

Diameter of the hole at final temperature is 929 mm.