Question

A steel scale is correct at 0°C. The length of a brass tube measured by it at 40°C is 4.5m. The correct length of the tube at 0°C is: (Coefficients of linear expansion of steel and brass are 11x10^-6/°C and 19x10^-6/°C respectively). Options: 1. 4.001m 2. 5.001m 3. 4.999m 4. 4.501m​

Answer 1

Answer:

The change in temperature (ΔT) = 70oC – 20oC = 50oC

The original length (L1) = 40 cm

Coefficient of linear expansion for steel (α) = 12 x 10-6 (Co)-1

Wanted : The change in length (ΔL) and the final length (L2)

Solution :

a) The change in length (ΔL)

ΔL = α L1 ΔT

ΔL = (12×10-6 oC-1)(40 cm)(50oC)

ΔL = (10-6)(24 x 103) cm

ΔL = 24 x 10-3 cm

ΔL = 24 / 103 cm

ΔL = 24 / 1000 cm

ΔL = 0.024 cm

b) The final length (L2)

L2 = L1 + ΔL

L2 = 40 cm + 0.024 cm

L2 = 40.024 cm