a silver bar 0.125 meter long is subjected to a temperture change from 200 degree celsius to 100 degree celsius. What will be the lenght of the bar after the temperture change?
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To find the change in length of the silver bar, we can use the thermal expansion equation. The equation for linear thermal expansion is given by:
ΔL = α * L * ΔT
Where:
- ΔL is the change in length
- α is the coefficient of linear expansion
- L is the original length
- ΔT is the change in temperature
The coefficient of linear expansion for silver is typically given as 0.0000185 °C^(-1). So, plugging in the given values, we have:
ΔL = (0.0000185 °C^(-1)) * (0.125 meter) * (100 °C - 200 °C)
Simplifying the calculation within the parentheses:
ΔL = (0.0000185 °C^(-1)) * (0.125 meter) * (-100 °C)
Now, we can multiply the values:
ΔL = (-0.0000185 °C^(-1)) * (0.125 meter) * (100 °C)
Calculating the expression within the parentheses:
ΔL = (-0.0000185 °C^(-1)) * (0.125 meter) * (-100 °C)
Simplifying the expression gives:
ΔL = 0.0000185 * 0.125 * 100
Finally, calculating the value:
ΔL ≈ 0.00023125 meters
To find the final length of the bar after the temperature change, we need to add the change in length to the original length:
Final Length = Original Length + ΔL
Final Length = 0.125 meter + 0.00023125 meters
Calculating the sum:
Final Length ≈ 0.12523125 meters
Therefore, the length of the silver bar after the temperature change from 200 °C to 100 °C is approximately 0.12523125 meters.