Question

A steel scale measures the length of a copper
wire as 80.0 cm, when both are at 20°C (the
calibration temperature for scale). What would
be the scale read for the length of the wire
when both are at 40°C? (Given Osteel
=11x10^-6 per°C and copper = 17x10^-6 per °C)​

Answer 1

Answer:

The answer will be 80.0096 cm

Explanation:

According to the problem the length of the copper wire is measure by the scale at the temperature of  20°C is given,

Now  when the temperature increased the both the things will expand,

Let the length of the wire after expanding is L'(c)

L'(c) = L+ (1+α(c) ΔT)

Let the length of the scale after expanding is L'(s)

L'(s) = L+ (1+α(s) ΔT)

Now the apparent length of the wire,

L(ap) = L'(c) -L'(s)

        = ( L+ (1+α(c) ΔT)) - ( L+ (1+α(s) ΔT))

        =   L(α(c) -α(s) ) ΔT

         = 80((17×10^(−6)−11×10^(−6))×20

        = 80.0096 cm