Page 59 - CITS - WCS - Mechanical

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Related Calculations
Example 1
A rod of length 5 m heated to 40°C. If the length increases to 7 m after some time.
Fine the expansion coefficient. Room temperature is 30°C.
Solution

Given
Initial length Lo = 5 m,
Expanded length L = 7 m
Changes in length Δ L = 7 – 5 = 2 m

Temperature difference Δ T = 40°C – 30°C = 10°C
Absolute temperature T = 10°C + 273=283 K
The linear expansion formula is given by,
∆L/(L°) = αLΔT
\ Length expansion coefficient is given by,

αL=∆L/(L°×ΔT)
= 2/ 5 x 283
αL= 14 x 10-4 K-1
Where,

A = original area,
ΔA = change in the area,
αA = area expansion coefficient,
ΔT = temperature difference,
A0 = expanded area.
Example 1

A rod of length 5 m heated to 40°C. If the length increases to 7 m after some time. Find the expansion coefficient.
Room temperature is 30°C.
Solution

Given:
Initial length Lo = 5 m,
Expanded length L = 7 m
Change in length Δ L = 7 – 5 = 2 m

Temperature difference Δ T = 40°C – 30°C = 10°C
Absolute temperature T = 10°C +273=283

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CITS : WCS - Mechanical - Exercise 3