A steel tape measures the length of a copper rod as 920 mm when the temperature is 280 K. Calculate the reading at 370 K. The linear expansion coefficient of copper is 17 × 10-6/K and that for steel 11 × 10-6/K. Assume that the steel tape reads correctly at 280 Κ.

Answer 1

First, we need to calculate the increase in length of the copper rod due to the change in temperature from 280 K to 370 K.

ΔL_copper = α_copper * L_initial_copper * ΔT
ΔL_copper = 17 × 10^-6/K * 920 mm * (370 K - 280 K)
ΔL_copper = 17 × 10^-6/K * 920 mm * 90 K
ΔL_copper = 0.00155 mm

Next, we need to calculate the increase in length of the steel tape due to the change in temperature from 280 K to 370 K.

ΔL_steel = α_steel * L_initial_steel * ΔT
ΔL_steel = 11 × 10^-6/K * 920 mm * (370 K - 280 K)
ΔL_steel = 11 × 10^-6/K * 920 mm * 90 K
ΔL_steel = 0.00102 mm

Since the steel tape reads correctly at 280 K, the total increase in length that the steel tape will show at 370 K will be:

Total increase = ΔL_steel + ΔL_copper
Total increase = 0.00155 mm + 0.00102 mm
Total increase = 0.00257 mm

Therefore, the reading on the steel tape at 370 K will be:
Reading at 370 K = L_initial_copper + Total increase
Reading at 370 K = 920 mm + 0.00257 mm
Reading at 370 K = 920.00257 mm

So, the reading on the steel tape at 370 K would be 920.00257 mm.