The bath

Dad poured 50 liters of water at 60°C into the tub. How much cold water must be added at 10°C to obtain a bath that has a temperature of 40°C?

Correct answer:

V₂ =  33.3333 l

Step-by-step explanation:

$$\begin{gathered} V_1=50\text{ l } \\ {t}_1=60\text{ °C } \\ {t}_2=10\text{ °C } \\ t=40\text{ °C } \\ Q=m\cdot c\cdot (t-t_0) \\ m=\rho V \\ Q=\rho V\cdot c\cdot (t-t_0) \\ {Q}_1+Q_2=Q \\ \rho \cdot V_1\cdot c\cdot (t_1-t_0)+\rho \cdot V_2\cdot c\cdot (t_2-t_0)=\rho \cdot (V_1+V_2)\cdot c\cdot (t-t_0) \\ {V}_1\cdot (t_1-t_0)+V_2\cdot (t_2-t_0)=(V_1+V_2)\cdot (t-t_0) \\ {V}_1\cdot t_1+V_2\cdot t_2=(V_1+V_2)\cdot t \\ 50\cdot 60+V_2\cdot 10=(50+V_2)\cdot 40 \\ 30V_2=1000 \\ {V}_2={\displaystyle \frac{100}{3}}\doteq 33.333333=33.3333\text{ l} \end{gathered}$$

Try another example

Showing 2 comments:

Melinda

Find the change in temperature if the temperature rises from −26°F to 15°F

8 months ago  Like

Doktor Matematiky

Melinda - change of temps is 15 - (-26) = 41 °F

8 months ago  Like

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