NECO 2000 Physics · Question 2

400g of cold water is added to 200g of water at 70°C. If they are properly mixed and the temperature of the…

Question

400g of cold water is added to 200g of water at 70°C. If they are properly mixed and the temperature of the mixture is 30°C. calculate the initial temperature of the cold water. (Neglect the heat absorbed by the container)

A.10°C
B.15°C
C.20°C
D.30°C
E.40°C

Answer: A. 10°C

Explanation written with AI and checked against the answer key

Analyze the question: Cold water (400 g) is mixed with hot water (200 g at 70°C). The final temperature is 30°C. We need the initial temperature of the cold water. Concept: By the principle of conservation of heat energy (method of mixtures): Heat lost by hot water = Heat gained by cold water Using Q = mcΔθ, and since both are water, the specific heat capacity c cancels out. Solution: Heat lost by hot water = 200 × c × (70 − 30) = 200 × 40 × c = 8000c Heat gained by cold water = 400 × c × (30 − θ) Equate them: 400(30 − θ) = 8000 30 − θ = 20 θ = 10°C Check: Cold water rises from 10°C to 30°C, a gain of 20°C, so 400 × 20 = 8000. Hot water falls from 70°C to 30°C, a loss of 40°C, so 200 × 40 = 8000. ✓ Answer: A. 10°C Tip: When the same liquid is mixed, c cancels, so just use m₁Δθ₁ = m₂Δθ₂. Here the cold water has twice the mass, so its temperature change is half that of the hot water (20°C vs 40°C). This shortcut helps you check quickly.

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