6. (15 points) A metal bar with a temperature of $20{ }^{\circ} \mathrm{C}$ was submerged into water taken at a temperature of $80{ }^{\circ} \mathrm{C}$. After thermal equilibrium was established, the temperature was found to be $60{ }^{\circ} \mathrm{C}$. After this, without removing the first bar from the water, another identical bar with a temperature of 20 ${ }^{\circ} \mathrm{C}$ was submerged into the water. What will the temperature of the water be after thermal equilibrium is established?
Answer: $50^{\circ} \mathrm{C}$.

Solution. The thermal balance equation in the first case is $c_{\mathrm{B}} m_{\mathrm{B}} 20=c_{\text {b }} m_{\text {b }} 40$. The thermal balance equation in the second case is

$$
c_{\mathrm{B}} m_{\mathrm{B}}(60-t)+c_{6} m_{6}(60-t)=c_{6} m_{6}(t-20) .
$$

We get $c_{6} m_{6} \cdot 2 \cdot(60-t)+c_{6} m_{6}(60-t)=c_{6} m_{\text{b}}(t-20)$. In the end, $t=50^{\circ} \mathrm{C}$.

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