A metre scale made up of aluminium (αa = 24 × 10-6/°C) measures length of a steel rod (αs = 12 × 10-6/°C) at room temperature as 50.00 cm. Now the temperature of the room is increased by 100 °C. What can be said about the measured length of the rod at new temperature?
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At new temperature T °C,
change in length of rod is,
∆LS = L0(αS∆T) = 50.00(12 × 10-6 × 100)
= 0.06 cm.
Hence, the actual length of rod at T °C,
LS = 50.06 cm
Due to change in temperature, along with rod, the scale will also increase in length.
For aluminium, at T °C,
∆La = L0(αa∆t) = 100.00 × 24 × 10-6 × 100
= 0.24 cm
∴ Length of the scale will be,
La = 100.24 cm
As, the expansion in scale is more than that in rod, the reading recorded by the scale at t°C will be less than 50 cm.