calculate the length which corresponds to a temperature of 10°C has a linear expansivity of 2*10^-5K^-1. calculate the length of the wire at a temperature of -10°C?
To calculate the length of the wire at a temperature of -10°C, we can use the formula for linear expansion:
ΔL = α*L*ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length of the wire
ΔT is the change in temperature
Given that the linear expansivity is α = 2*10^-5 K^-1 and the initial temperature is 10°C, we can calculate the change in temperature:
ΔT = -10°C - 10°C = -20°C
Now we can substitute the values into the formula to find ΔL:
ΔL = (2*10^-5 K^-1) * L * (-20°C)
To calculate the length of the wire at -10°C, we need to find the sum of the initial length L and ΔL:
Length = L + ΔL
Let's calculate ΔL first:
ΔL = (2*10^-5 K^-1) * L * (-20°C)
= -0.0004 * L
Now we can substitute the value of ΔL into the formula to find the length at -10°C:
Length = L + ΔL
= L + (-0.0004 * L)
= L(1 - 0.0004)
Simplifying further, we get:
Length = L * 0.9996
Therefore, the length of the wire at -10°C is 0.9996 times the original length (L).