SME
Grade 6 Science · Problem type
Mix hot and cold water
Use this for “Equal cups of 80 °C and 20 °C water are mixed. What is the temperature?”
Diagram
Hot water: 80 °C
Mixed water: 50 °C
Cold water: 20 °C.
This is an example. Type your own values to start a new problem.
(
h (°C)
+
c (°C)
)
÷
2
=
m (°C)
Formulas
(80 + 20) ÷ 2 = 50
(Hot + cold) ÷ 2 = mixed temperature
Assumptions
•
Thermal energy moves from the hot water to the cold water until they are the same temperature.
•
With equal amounts, the hot water cools as much as the cold water warms: the mix ends halfway between.
•
Halfway is the average: add the two temperatures and divide by 2.
Step-by-step
WE KNOW
Hot water: 80 °C
Cold water: 20 °C
FIND
mixed water
Step 1 · Find mixed water
(80 + 20) ÷ 2 = ?
(Hot + cold) ÷ 2 = mixed temperature
The hot cup gives what the cold cup gains, so the mix is the average of the two.
Mixed water = 50 °C (the hot water cooled 30 °C; the cold water warmed 30 °C)
Check
Put the numbers back in. Both sides should match.
50 − 20 = 80 − 50 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.