Respuesta :
Answer:
Explanation:
To measure increase in length due to thermal expansion, the formula is
L₂ =L₁ ( 1 + α t ) where L₁ length increases to L₁ due to rise in temperature by t.
L₂ in both the case is same so
for aluminium
L₂ = 2.8 ( 1 + 23 X 10⁻⁶ t )
for steel
L₂ = 2.804 ( 1 + 12 X 10⁻⁶ t )
2.8 ( 1 + .000023t) = 2.804 ( 1 + .000012 t )
Solving this equation
t = 122C
Final temperature of both = 122 +20 = 142 C
Answer:
Temperature on the shaft [tex]142 C[/tex]
Explanation:
Given:
Diameter of the ring [tex]2.8cm[/tex]
Temperature [tex]20^{o} c[/tex]
To measure increase in length due to thermal expansion, the formula is
[tex]$L_{2}=L_{1}(1+\alpha t)$[/tex] where [tex]$L_{1}$[/tex] length increases to [tex]$L_{1}$[/tex] due to rise in temperature by t.
[tex]$\mathrm{L}_{2}$[/tex] in both the case is same so
for aluminium
[tex]$\mathrm{L}_{2}=2.8\left(1+23 \times 10^{-6} \mathrm{t}\right)$[/tex]
for steel
[tex]$L_{2}=2.804\left(1+12 \times 10^{-6} t\right)$[/tex]
[tex]$2.8(1+.000023 t)=2.804(1+.000012 t)$[/tex]
Solving this equation
[tex]$\mathrm{t}=122 \mathrm{C}$[/tex]
Final temperature of both [tex]$=122+20=142 \mathrm{C}$[/tex]
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