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Jack enjoys drinking green tea at 60°C.
He pours 200 mL of 90°C green tea into a cup and then adds 4°C chilled water to the same cup to cool it down.
What is the minimum amount of chilled water, to the nearest mL, required to cool Jack's green tea to 60°C? (4 marks)
(Assume the green tea is essentially water and no energy is lost to the surroundings)
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\(107\ \text{mL}\)
→ The energy contained in the temperature of the green tea that is lost to reduce it to 60°C needs to be used to heat up the chilled water from 4°C to 60°C.
→ Green tea’s change in temperature \(=90^{\circ}-60^{\circ}=30^{\circ}\).
→ The energy that needs to be lost from the green tea can be quantised:
\(Q=mc\Delta t=200 \times 4.18 \times -30=-25\ 080\ \text{J}\)
→ This \(25\ 080\ \text{J}\) then goes into heating up a required amount of chilled water from \(4^{\circ}\) to \(60^{\circ}\).
| \(Q\) | \(=mc\Delta t\) | |
| \(25\ 080\) | \(=m \times 4.18 \times 56\) | |
| \(m\) | \(=\dfrac{25\ 080}{4.18 \times 56}\) | |
| \(=107\ \text{g}\) | ||
| \(=107\ \text{mL}\) |