Final answer:
To find out how much water was in the bucket, one needs to use the principle of conservation of energy in a calorimetry context. The heat lost by the iron pan when cooled to 20°C is equal to the heat gained by the water that is heated up to 20°C. By equating these two quantities and solving for the mass of the water, we get the answer.
Step-by-step explanation:
The student is asking how much water (in grams) was in the bucket given that an iron pan was heated and transferred into it causing a change in temperature. This is a typical calorimetry problem that involves calculating heat transfer. To solve this problem, the heat gained by the water (which will be equal in magnitude and opposite in sign to the heat lost by the iron pan) must be calculated using the specific heat capacity formula: Q = m * Cp * ΔT For the iron pan: m (mass of iron pan) = 3000g Cp (specific heat capacity of iron) = 0.44 J/gC ΔT (change in temperature of iron pan) = 350 C - 20 C Q (heat lost by iron pan) = 3000g * 0.44 J/gC * (350 C - 20 C) For the water: m (mass of water) = unknown, we will calculate this Cp (specific heat capacity of water) = 4.184 J/gC (standard) ΔT (change in temperature of water) = 20 C - 17 C Q (heat gained by water) = m * 4.184 J/gC * (20 C - 17 C) Since the heat lost by the iron pan is equal to the heat gained by the water: 3000g * 0.44 J/gC * (350 C - 20 C) = m * 4.184 J/gC * (20 C - 17 C) We then solve for m (mass of water) using the given equation