The bath

The bath has water with a volume of 220 l and a temperature of 65°C. Determine the mass m₂ of water at 15°C to be poured so that the resulting temperature of the water in the bath is 40°C. We neglect the heat exchange between water and the environment. The mass heat capacity of water is 4200 J/kg ∙ °C.

Correct answer:

m₂ =  220 l

Step-by-step explanation:

$$\begin{gathered} m_1=220\text{ l } \\ {t}_1=65\text{ l } \\ c=4200{\text{J/kg/}}^{\circ }\text{C } \\ {t}_2=15^{\circ }\text{C } \\ t=40^{\circ }\text{C } \\ {Q}_1+Q_2=Q \\ {m}_1\cdot c\cdot t_1+m_2\cdot c\cdot t_2=(m_1+m_2)\cdot c\cdot t \\ {m}_1\cdot t_1+m_2\cdot t_2=(m_1+m_2)\cdot t \\ 220\cdot 65+m_2\cdot 15=(220+m_2)\cdot 40 \\ 25m_2=5500 \\ {m}_2=220\text{ l} \end{gathered}$$

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