Question

3. (8 pts.) A tube made out of a mystery metal has a length of 1.2475 m when its temperature is 22.005°C. When the tube is heated to a temperature of 97.842"c, its length is measure to be 1.2490 m. Find the metal's coefficient of thermal expansion, a.

Answer 1

Solution) L1 = 1.2475 m

T1 = 22.005°C

T2 = 97.842°C

L2 = 1.2490 m

Coefficient of thermal expansion , alpha = ?

Let alpha be denoted by A

L2 = L1( 1 + A(dT))

Here dT = T2 - T1 = 97.842 - 22.005 = 75.837°C

1.2490 = 1.2475(1 + A(75.837))

1 + A(75.837) = (1.2490)/(1.2475)

1 + A(75.837) = 1.0012

A(75.837) = 1.0012 - 1

A(75.837) = 0.0012

A = (0.0012)/(75.837)

A = 1.5823×10^(-5) /°C