Answer:
m₁ = 5.507 x 10⁻³ kg = 5.507 g
Explanation:
The heat released by the steam must be absorbed by the melting wax, according to the law of conservation of energy:
Heat Released by Steam = Heat Absorbed by Wax
Latent Heat of Fusion of Steam = Heat Absorbed by Wax + Latent Heat of Fusion of Wax
m₁H₁ = m₂CΔT₂ + m₂H₂
where,
m₁ = mass of water = ?
H₁ = Latent Heat of Fusion of Water = 2260 KJ/kg = 2.26 x 10⁶ J/kg
m₂ = mass of wax = 50 g = 0.05 kg
C = specific heat capacity of wax = (0.7 cal/g°C)(1000 g/1 kg)(4.184 J/1 Cal)
C = 2928.8 J/kg.°C
ΔT₂ = Change in Temperature of Wax = 55°C - 20°C = 35°C
H₂ = Latent Heat of Fusion of Wax = (35 cal/g)(1000 g/1 kg)(4.184 J/1 Cal)
H₂ = 146440 J/kg
Therefore,
m₁(2.26 x 10⁶ J/kg) = (0.05 kg)(2928.8 J/kg.°C)(35°C) + (0.05 kg)(146440 J/kg)
m₁ = (5125.4 J + 7322 J)/2.26 x 10⁶ J/kg
m₁ = 5.507 x 10⁻³ kg = 5.507 g
