The steel tape will indicate a length of approximately 95.33 cm for the brass rod at 55.0°C.
What will the tape indicate for the length of the rod when the rod and the tape are at 55.0°C?
ΔL brass = α brass * L 0 * ΔT
where:
ΔL brass is the change in length of the brass rod
L 0 is the initial length of the brass rod at 20.0°C (95.00 cm)
ΔT is the change in temperature (55.0°C - 20.0°C = 35.0°C)
ΔL brass = 18.6 x 10⁻⁶ °C⁻¹ * 95.00 cm * 35.0°C
ΔL brass ≈ 0.73 cm
ΔL steel = α steel * L 0 * ΔT
ΔL steel = 11.7 x 10⁻⁶ °C⁻¹ * 95.00 cm * 35.0°C
ΔL steel ≈ 0.40 cm
The apparent length of the rod as measured by the steel tape will be the sum of the initial length and the change in length of the brass rod minus the change in length of the steel tape (since steel expands less than brass).
Apparent length = L 0 + ΔL brass - ΔL steel
Apparent length = 95.00 cm + 0.73 cm - 0.40 cm
Apparent length ≈ 95.33 cm
Therefore, the steel tape will indicate a length of approximately 95.33 cm for the brass rod at 55.0°C.