Ancient Water Boiler

In old times, hot stones were placed in water to heat it up. Consider five hot stones (granite) with a temperature of $500^\circ\mathrm{C}$ and a mass of $100\,\mathrm{g}$ each placed in a bucket with $5\,\mathrm{l}$ of water. The initial water temperature is $20^\circ\mathrm{C}$. What is the mixing temperature afterward? The heat capacity of the stones is given as $0.790 \mathrm{kJ/(kg\,K)}$. Solution

We can use simply the formula for the mixing temperature given as $$T_\mathrm{M} = \frac{m_1c_1T_1 + m_2c_2T_2}{m_1c_1 + m_2c_2}$$ Now we assign index 1 to the water bucket and 2 to the stones. The mass of the water was given as 5 kg. It is very important to insert all temperatures in Kelvin. This leads to $T_1 = 293.15\,\mathrm{K}$ for the water and $T_2 = 873.5\,\mathrm{K}$. The mixing temperature is then given as $$T_\mathrm{M} = 61.4^\circ\mathrm{C}$$

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Last modified: 2022-10-01 20:59:48 by mustafa

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Ancient Water Boiler