a silver bar 0.125 meter long is subjected to a temperature change from 2oo degrees celsius to 100 degrees Celsius what will the length of the bar be after the temperature change
L = Lo + a/oC(T-To)*Lo
L = 0.125 + 1.9*10^-6(100-200)0.125 =
0.124976
To determine the length of the silver bar after the temperature change, we can use the concept of thermal expansion.
Thermal expansion is the tendency of matter to change in shape, volume, or length in response to a change in temperature. It occurs because the particles in a substance move more vigorously as the temperature increases, causing them to spread apart.
In this case, we need to know the coefficient of linear expansion for silver. The coefficient of linear expansion, denoted by α, is a property specific to each material. It describes the relative change in length per degree Celsius of temperature change.
The coefficient of linear expansion for silver is approximately 0.000019 per degree Celsius.
Given:
Length of the silver bar before the temperature change (L₀) = 0.125 meters
Temperature before the change (T₀) = 200 degrees Celsius
Temperature after the change (T₁) = 100 degrees Celsius
To calculate the change in length (ΔL), we can use the formula:
ΔL = α * L₀ * (T₁ - T₀)
Substituting the values into the formula:
ΔL = 0.000019 * 0.125 * (100 - 200)
Simplifying the calculation:
ΔL = 0.000019 * 0.125 * (-100)
ΔL ≈ -0.00002375 meters
Since the result is negative, it means that the length of the silver bar will contract.
The final length of the bar (L₁) after the temperature change can be found by subtracting the change in length from the initial length:
L₁ = L₀ - ΔL
L₁ = 0.125 - (-0.00002375)
L₁ ≈ 0.125 + 0.00002375
L₁ ≈ 0.12502375 meters
Therefore, the length of the silver bar after the temperature change will be approximately 0.12502375 meters.