a steel rod when measured with a zinc scale both being at 25 degree Celsius appear to be one meter long.if the zinc scale is correct at 0 degree Celsius, what is the actual length of the rod at 0 degree Celsius? [linear expansivity of steel=12*10^-6 /degree C

linear expansivity of zinc=26*10^-6/degree Celsius]

I need solution

I need this solution.

To find out the actual length of the steel rod at 0 degree Celsius, we'll need to account for the expansion of both the steel rod and the zinc scale.

Let's denote the original length of the steel rod at 0 degree Celsius as L0. We know that the length of the rod at 25 degree Celsius (L25) is 1 meter.

First, we'll calculate the expansion of the steel rod from 0 to 25 degree Celsius using its linear expansivity:

ΔL_steel = α_steel * L0 * ΔT

where α_steel is the linear expansivity of steel and ΔT is the change in temperature (25°C - 0°C = 25°C).

ΔL_steel = (12 * 10^-6 /°C) * L0 * 25

Next, we'll calculate the expansion of the zinc scale from 0 to 25 degree Celsius using its linear expansivity:

ΔL_zinc = α_zinc * L0 * ΔT

where α_zinc is the linear expansivity of zinc.

ΔL_zinc = (26 * 10^-6 /°C) * L0 * 25

Now, we can determine the actual length of the steel rod at 0 degree Celsius by subtracting the expansions from the measured length at 25 degree Celsius:

L0 = L25 - ΔL_steel - ΔL_zinc
L0 = 1 - ΔL_steel - ΔL_zinc

Substituting the previously calculated values, we can find the actual length of the rod at 0 degree Celsius.

Please note that the linear expansivity values and temperature difference used in this explanation are assumed for illustrative purposes only and may not reflect the actual values specific to the materials being discussed.