2.0 kg of water at 80 °C is poured into 3.0 kg of water at 20 °C in an insulated container. Calculate the final equilibrium temperature.

Thermodynamics Challenge #2 — Thermal Equilibrium

Mixing hot
and cold water.

Thermodynamics Hard

Problem

In an insulated container, 2.0 kg of water at 80 °C is poured into 3.0 kg of water at 20 °C. Calculate the final equilibrium temperature of the mixture.

Hot water\( 2.0\ \mathrm{kg}\ \mathrm{at}\ 80\ ^{\circ}\mathrm{C} \)
Cold water\( 3.0\ \mathrm{kg}\ \mathrm{at}\ 20\ ^{\circ}\mathrm{C} \)
Containerinsulated (no losses)
Answer in°C

Both are water — think about what that does to the specific heat capacity.

Hint: heat lost by the hot water equals heat gained by the cold: \( m_1 c (T_1 - T_f) = m_2 c (T_f - T_2) \). Notice what cancels before you touch a calculator.

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°C

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Mixing hotand cold water.

Problem

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Mixing hot
and cold water.