Question Detail
Question
How much heat input is needed to raise the temperature of a 20 kg vat made of iron and filled with 3 kg of water from 10°C to 90°C? Take the specific heat capacity of iron and water to be 450 J/kg·°C and 4186 J/kg·°C respectively.
Correct Answer
Option A is the correct answer.
Detailed Explanation
The total heat required is the sum of heat for the iron vat and for the water. Q = m_iron × c_iron × ΔT + m_water × c_water × ΔT = (20 kg × 450 J/kg·°C × 80°C) + (3 kg × 4186 J/kg·°C × 80°C) = (20 × 450 × 80) + (3 × 4186 × 80) = (720,000) + (1,004,640) = 1,724,640 J = 1.72464 MJ ≈ 1.72 MJ.
Hint
Calculate heat for each substance using Q = mcΔT, then add them together.