Question

11. A wire made of silver has coefficient of linear expansion, 29x10-6/k and length of 10m. A square metal plate made of such silver and side length 10m expands as its temperature changes from 25°C to 78°C. Determine the ratio of the area of the square and length of the metal plate and length at the final temperatures.​

Answer 1

By using the coefficient of linear expansion, the increase in the length of the metal plate is by 0.015m and in the area is by 0.3074$m^2$.

The rate of change in length of a metal per degree change in temperature is known as the coefficient of linear expansion.

Given:

Coefficient of linear expansion, α = 29 x $10^-^6$/k

Length, L1 = 10m

T1 = 25℃

T2 = 78℃

ΔT = 78 – 25 = 53℃

To find:

Change in length (ΔL) and area (ΔA) of metal plate = ?

Formula:

ΔL = α L1 ΔT

ΔA = A1 2 α ΔT

Calculations:

ΔL = 29 x $10^-^6$ x 10 x 53

ΔL = 0.01537m

ΔA = 100 x 2 x 29 x $10^-^6$ x 53

ΔA = 0.3074$m^2$

A2 = 100.3074$m^2$

Result:

The increase in the length and area is by 0.015m and 0.3074$m^2$ respectively.

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