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 reading for the length of the wire when both are at
40°C?
[asteel = 11x10°7°C, Oopper = 17x10/c]
2) 80.0272 cm
1) 80.0096 cm
4) None
3) 79.9884 cm​

Answer 1

Explanation:

According to the question

the length of the copper wire at the temperature of  20°C is given, L=80cm

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,

Lapparent=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

        =80.0096cm