Explanation:
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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
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Given:
m₁ = 1540 g, mass of iron horseshoe
T₁ = 1445 °C, initial temperature of horseshoe
c₁ = 0.4494 J/(g-°C), specific heat
m₂ = 4280 g, mass of water
T₂ = 23.1 C, initial temperature of water
c₂ = 4.18 J/(g-°C), specific heat of water
L = 947,000 J heat absorbed by the water.
Let the final temperature be T °C.
For energy balance,
m₁c₁(T₁ - T) = m₂c₂(T - T₂) + L
(1540 g)*(0.4494 J/(g-C))*(1445-T C) = (4280 g)*(4.18 J/(g-C))*(T-23.1 C) + 947000 J
692.076(1445 - T) = 17890(T - 23.1) + 947000
10⁶ - 692.076T = 17890T - 413259 + 947000
466259 = 18582.076T
T = 25.09 °C
Answer: 25.1 °C
