A blacksmith plunges a 2 kg horseshoe at 400 °C into 1 kg of water at

1.	A blacksmith plunges a 2 kg horseshoe at 400 °C into 1 kg of water at 20 °C. Find the maximum temperature of the water. [Specific heat of iron = 0.11 kcal/(kg-°C)]
Answer» Data: mx = 2 kg, c₁ = 0.11 kcal/(kg.°C), T₂ = 400 °C, m₂ = 1 kg, c₂ = 1 kcal/(kg.°C), T₂ = 20 °C, T = ? Heat lost by the horseshoe = heat gained by the water ∴ m₁ c₁ (T₁ – T) = m₂ c₂(T – T₂ ) ∴ 2 kg × 0.11 kcal/(kg.°C) × (400 °C – T) = 1 kg × 1 kcal/(kg.°C) × (T – 20 °C) ∴ 0.22 × (400 °C – T) = T – 20 °C ∴ 1.22 T= 108 °C ∴ T = \(\cfrac{108}{1.22}\) °C = 88.52 °C Maximum temperature of the water = 88.52 °C.

A blacksmith plunges a 2 kg horseshoe at 400 °C into 1 kg of water at 20 °C. Find the maximum temperature of the water. [Specific heat of iron = 0.11 kcal/(kg-°C)]

Answer»

Data: mx = 2 kg,

c₁ = 0.11 kcal/(kg.°C), T₂ = 400 °C, m₂ = 1 kg,

c₂ = 1 kcal/(kg.°C), T₂ = 20 °C, T = ?

Heat lost by the horseshoe = heat gained by the water

∴ m₁ c₁ (T₁ – T) = m₂ c₂(T – T₂ )

∴ 2 kg × 0.11 kcal/(kg.°C) × (400 °C – T)

= 1 kg × 1 kcal/(kg.°C) × (T – 20 °C)

∴ 0.22 × (400 °C – T) = T – 20 °C

∴ 1.22 T= 108 °C

∴ T = \(\cfrac{108}{1.22}\) °C = 88.52 °C

Maximum temperature of the water = 88.52 °C.