Given:
The initial dimensions of the manganese sheet, 20 cm×30 cm⟹ Initial area, A0=20×30=600 cm2
Increase in the area, ΔA=0.72 cm2
The rise in temperature, ΔT=75−25=50 ∘C
We know that the coefficient of superficial thermal expansion, β is given by:
β=ΔAA0ΔT
⟹βMn=0.72600×50
⟹βMn=2.4×10−5 ∘C−1
⟹βMn=24×10−6 ∘C−1