A wire of length 10m is cooled from 50oC to 10oC. Calculate the decrease in the length of the wire. [c = 3 x 10-5K-1]
1.8 x 10-4m
1.5 x 10-4m
1.2 x 10-2m
1.8 x 10-3m
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c = 3×10^-5
∆temp. = 50°-10°=40°
L0= 10
L1=x
c = L1-L0/L0 (∆temp)
3× 10^-5=x-10/10(40)
3×10^-5= x-10/400
3×10^-5 × 400= x-10
0.012=x-10
x = 0.012+10
x= 10.012
x= 1.2×10^-2
Hope you understand
To calculate the decrease in the length of the wire as it cools down, we can use the formula for thermal expansion:
ΔL=L0×α×ΔT
Where:
ΔL is the change in length,
L0 is the original length of the wire (10 m in this case),
α is the coefficient of linear expansion (given as 3×10−5K−1),
ΔT is the change in temperature (initial temperature minus final temperature).
Substitute the given values into the formula:
ΔL=10m×(3×10−5K−1)×(50∘C−10∘C)
ΔL=10m×(3×10−5K−1)×40∘C
ΔL=10m×(1.2×10−3K−1)
ΔL=1.2×10−2m
So, the decrease in the length of the wire is1.2cm
We will use the formula
for linear expansion
Change in length = coefficient
of linear expansion × original
length × change in temp
REFERENCE TO THE QUESTION:
Temperature change =
50°C-10°C = 40°C
Decrease in length =
(3×10^-5 K-1) × (10m) ×
(40°C)=1.2 × 10^-2
