This is done by using the same mass and realizing that the specific heat of normal water and hot water is the same. In our procedure, 100 ml of hot water was mixed with 100 ml of normal water; therefore, the masses in Equation 3 cancel out (the densities of water at different temperatures are not exactly the same, but the difference is negligible). This leads to the temperature change of the hot water being equal to the negative temperature change in the normal water, shown as: (4) Using equation 4, it can be deduced that the initial temperature of the hot water minus the temperature change of the mixture equals the cold water temperature plus the temperature change of the mixture (Equation 5). This is then rearranged to mean that the initial temperature of the hot water is twice the temperature change plus the initial temperature of the normal water. This is shown in the equation 6.
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