Knowing that the combustion of 30.0 ml of kerosene produces enough heat to heat and melt 10.0 kg

Knowing that the combustion of 30.0 ml of kerosene produces enough heat to heat and melt 10.0 kg of silver, determine the initial temperature of silver.

Q1 = Q2 + Q3.
Q1 (kerosene combustion) = q * m1, where q = 4.6 * 107 J / kg), m1 = ρ * V (ρ = 800 kg / m3, V = 30 ml = 30 * 10-6 m3).
Q2 (silver melting) = λ * m2, where λ = 0.87 * 105 J / (kg * K), m2 = 10 kg.
Q3 (heating silver) = С * m2 * (tmelt – tn), where С = 250 J / (kg * K), tm = 962 ºС).
q * m1 = λ * m2 + С * m2 * (tpl – tn).
4.6 * 107 * 800 * 30 * 10-6 = 0.87 * 105 * 10 + 250 * 10 * (962 – tn).
250 * 10 * (962 – tн) = 234000.
962 – tn = 93.6.
tн = 868.4 ºС.
Answer: The initial temperature is 868.4 ºС.