Physics · Grades 10–12
Ideal mixing temperature
Both portions have the same constant specific heat; no phase change, container heating or loss.
Rule and assumptions
Both portions have the same constant specific heat; no phase change, container heating or loss.
Tf = (m₁T₁ + m₂T₂)/(m₁ + m₂)
Worked examples
Mix 8 kg at 24 °C with 2 kg at 58 °C of the same liquid. Assume equal constant specific heat, no phase change, negligible container heat capacity and no losses. Find equilibrium temperature. Round to 3 decimal places if needed. Answer in °C.
Tf = (m₁T₁ + m₂T₂)/(m₁ + m₂) (8 × 24 + 2 × 58) / (8 + 2) = 30.8
30.8 °C
Mix 8 kg at 27 °C with 8 kg at 68 °C of the same liquid. Assume equal constant specific heat, no phase change, negligible container heat capacity and no losses. Find equilibrium temperature. Round to 3 decimal places if needed. Answer in °C.
Tf = (m₁T₁ + m₂T₂)/(m₁ + m₂) (8 × 27 + 8 × 68) / (8 + 8) = 47.5
47.5 °C
Try two questions
Mix 2 kg at 29 °C with 10 kg at 73 °C of the same liquid. Assume equal constant specific heat, no phase change, negligible container heat capacity and no losses. Find equilibrium temperature. Round to 3 decimal places if needed. Answer in °C.
Mix 6 kg at 19 °C with 4 kg at 84 °C of the same liquid. Assume equal constant specific heat, no phase change, negligible container heat capacity and no losses. Find equilibrium temperature. Round to 3 decimal places if needed. Answer in °C.
Answers and reasoning
Answers and marking notes
- 65.667 °C
Tf = (m₁T₁ + m₂T₂)/(m₁ + m₂) (2 × 29 + 10 × 73) / (2 + 10) = 65.667
- 45 °C
Tf = (m₁T₁ + m₂T₂)/(m₁ + m₂) (6 × 19 + 4 × 84) / (6 + 4) = 45
Further reading and review references
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Learning preview · independent educational and translation review required. Suggested grades are not official curriculum alignment.