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.
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.