What happens to the temperature when you mix the water?
Explain a first model and change it when the tutor adds a detail.
The question
In a practice science interview, a tutor describes mixing two portions of water in an insulated cup. Assume the cup initially absorbs negligible heat. No heat escapes, and the portions reach the same temperature.
| Mass (g) | Temperature (°C) | |
|---|---|---|
| Cool water | 200 | 20 |
| Warm water | 100 | 50 |
The water in both portions has the same specific heat capacity.
“Find the final temperature and explain your reasoning aloud.”
Not saved by this site. Your browser may restore text when you navigate back.
A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: Choose the model
What would you do here? Open the move you’d make.
Balance heat lost and heat gained using both masses.
The strong move. Both portions are water, so their heat capacities are proportional to their masses.
Average the two starting temperatures.
Tempting, but it misses something. An unweighted average gives both portions the same heat capacity. The cool portion has twice the mass.
See how a strong candidate says it
“The heat the warm water loses equals the heat the cool water gains. I’ll use each mass and its change in temperature.”
Why it works: Both portions are water, so their heat capacities are proportional to their masses.
Step 2: Explain the result
What would you do here? Open the move you’d make.
Use 30 °C and check both sides of the heat balance.
The strong move. The warmer portion has half the mass and twice the temperature change.
Use 35 °C because each portion changes by 15 degrees.
Tempting, but it misses something. At 35 °C the cool water would gain twice as much heat as the warm water releases.
See how a strong candidate says it
“I get 30 °C. The 200 g portion warms by 10 degrees, while the 100 g portion cools by 20. Both products are 2,000 g·°C, so the heat transfer balances.”
Why it works: The warmer portion has half the mass and twice the temperature change.
Step 3: Use the hint
The tutor now says the cup began at 20 °C and has the same heat capacity as 100 g of water. The system still loses no heat to its surroundings.
What would you do here? Open the move you’d make.
Add the cup’s heat capacity to the cool side and solve again.
The strong move. The cup starts at 20 °C and absorbs some of the heat.
Keep 30 °C because the cup does not change the amount of water.
Tempting, but it misses something. At 30 °C the cool water uses all the heat the warm water releases. There is none left to warm the cup.
See how a strong candidate says it
“The cool side now acts like 300 g of water. At 27.5 °C, 100 × 22.5 equals 300 × 7.5. The heat lost balances the gain by the cool water and the cup.”
Why it works: The cup starts at 20 °C and absorbs some of the heat.
Step 4: Explain the change
What would you do here? Open the move you’d make.
Explain the direction and state the insulation and mixing assumptions.
The strong move. The direction follows from adding heat capacity on the cool side.
Say any cup with the same mass gives the same result.
Tempting, but it misses something. Cups with the same mass can have different specific heat capacities. The model uses heat capacity and starting temperature.
See how a strong candidate says it
“The cup needs heat too, so the final temperature moves closer to 20 °C. I assumed the cup and both portions reach a common temperature, with no heat escaping.”
Why it works: The direction follows from adding heat capacity on the cool side.
The answer, in short
- Decision
- Explain 30 °C first, then revise to 27.5 °C.
- Because
- Both results balance heat under their own assumptions.
- What would change it
- Heat exchange with the room would add another term to the balance.
Common traps
- Averaging temperatures without checking masses.
- Leaving the cup out after the tutor includes it.
Check your answer
- I chose a heat balance.
- I checked the first number.
- I used the new heat capacity.
- I explained why the temperature fell.
Last reviewed Nov 11, 2026