The Mixing Court

Why it matters

Pour hot into cold and the final temperature is not a guess — it's a verdict. Energy testifies, the calorimeter is the courtroom, and the books must balance to the joule.

The idea in plain words

The principle of calorimetry. Tap the terms.

m₁c(T₁−T) = m₂c(T−T₂)

150 g water at 90 °C + 100 g at 30 °C. Final temperature?

T = 66 °C

• conservation: principle — no heat escapes the mixture → heat lost by hot = heat gained by cold
• the apparatus: calorimeter — thin copper vessel, insulated, with stirrer and thermometer — built to keep the court honest
• exam favourite: why copper — low specific heat (absorbs little itself) and a great conductor (reaches equilibrium fast)
• 150(90−T) = 100(T−30)
• 13500 − 150T = 100T − 3000 → 250T = 16500

Predict first

100 g of water at 80 °C meets 200 g at 20 °C. The mixture settles nearest to…

Heat lost = heat gained: 100(80−T) = 200(T−20) → T = 40 °C. The final temperature is a mass-weighted verdict, not a midpoint.

• 40 °C — twice the cold mass drags it down toward 20 — correct
• 50 °C — always the average
• 60 °C

What you do

Set the two waters, commit your prediction, then pour. Get within 2 °C twice to win the court's respect.

Check yourself

A calorimeter is made of thin COPPER because copper…

It steals little of the heat being measured and spreads what it gets instantly — the ideal silent witness.

Equal masses of 80 °C and 20 °C water mix to give…

m(80−T) = m(T−20) → T = 50. Temperatures NEVER add; energy books just balance.

Stirring the mixture before reading the thermometer…

Without stirring you read a warm layer or a cold pocket, not the equilibrium.

• has low specific heat and conducts heat fast — correct
• is shiny
• never gets hot
• 50 °C — with equal masses, the midpoint is correct — correct
• 60 °C
• 100 °C — heats add up
• ensures one uniform temperature — a true verdict — correct
• adds significant heat
• cools the mixture down