A metal sphere of radius 3cm made of brass is heated from 30°C to 100°C , Calculate the initial and final volume of the
metal sphere (Iinear expansivity of brass =0.000019k-¹ and volume of sphere =⁴/3 πr³

Let:

r= radius= 3cm= 0.03m

∅1= initial temperature= 30°C

∅2= final temperature= 100°C

∆∅= change in temperature= ∅2 - ∅1= 70°C

L.E.= linear expansivity= 0.000019k^-1

¥= 3L.E.= volume expansivity= 3(0.000019)= 0.000057k^-1

The initial volume of the metal sphere= 4/3(πr³)

= 4/3(π×0.03³)

= 4(π×0.03²×0.01)

= 4(3.142×0.0003×0.01)

= 4(0.000009426)

= 0.000037704

= 3.7704 × 10^-5m³

¥= V2 - V1/V1∆∅

V2= ¥V1∆∅ + V1

= (1.5044 × 10^-7) + (3.7704×10^-5)

= 0.00003785

= 3.785 × 10^-5m³

Therefore, the initial and final volume of the metre sphere are 3.7704 × 10^-5 and 3.785 × 10^-5 respectively.

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