NEET-XII-Physics
23: Heat and Temperature
- #13A circular hole of diameter 2.00 cm is made in an aluminium plate at 0°C. What will be the diameter at 100°C? α for aluminium = 2.3 × 10-5 °C-1.Ans : Given:
Diameter of a circular hole in an aluminium plate at 0°C, d1 = 2 cm = 2 × 10-2 m
Initial temperature, t1 = 0 °C
Final temperature, t2 = 100 °C
So, the change in temperature, (`` \Delta ``t) = 100°C - 0°C = 100°C
The linear expansion coefficient of aluminium, αal = 2.3 × 10-5 °C-1
Let the diameter of the circular hole in the plate at 100oC be d2 , which can be written as:
`` {d}_{2}={d}_{1}\left(1+\alpha \Delta t\right)``
`` \Rightarrow {d}_{2}``= 2 × 10-2 (1 + 2.3 × 10-5 × 102)
`` \Rightarrow {d}_{2}``= 2 × 10-2 (1 + 2.3 × 10-3)
`` \Rightarrow {d}_{2}``= 2 × 10-2 + 2.3 × 2 × 10-5
`` \Rightarrow {d}_{2}`` = 0.02 + 0.000046
`` \Rightarrow {d}_{2}``= 0.020046 m
`` \Rightarrow {d}_{2}``≈ 2.0046 cm
Therefore, the diameter of the circular hole in the aluminium plate at 100oC is 2.0046 cm.
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