Question

An alumium rod when measured with a steel scale both being at 25 degree celcius appears to be 1 meter long. If the scale is correct at 0 degree celcius, what is the true length of the rod at 25 degree celcius? What wull be the length of rod at 0 degree celcius?

Answer 1

Given:

temperature at which the rod is measured= 25°

length of aluminium rod measured at 25°C= 1 meter

temperature at which the scale is correct= 0°C

Linear expansivity of steel= 12* 10^-6

linear expansivity of aluminum= 26* 10^-6

To find:

1. True length of rod at 25°C
2. Length of rod at 0°C

Solution:

1. Let the length of the aluminum and steel rod at 0°C be L0A and L0S respectively.

Length of the steel scale at 25°C , thermal expansion is:

LA25 = LA0(1+ (αS - αA)25)

LA0 = LA25/ (1+ (αS-αA)t)

LA0 = 100/ (1+ (12*10^-6 - 26*10^-6)25)

LA0 ≈ 100.05 cm at 0°C

   2. Let the length at 25°C of the aluminium trod be LA25

The actual measure of aluminum rod at 25°C, will be

LA25 = 100 * (1+ 26* 10^-6*25)

LA25 ≈ 100.06 cm