To solve this problem, we can use the principle of conservation of energy, which states that the total energy of a closed system remains constant. The energy lost by the hot liquid is gained by the cold water, so we can write:
Q_lost = Q_gained
where Q is the amount of heat transferred. We can express Q as:
Q = m * Cs * ΔT
where m is the mass of the substance, Cs is its specific heat capacity, and ΔT is the change in temperature.
Let's start by calculating the amount of heat lost by the hot liquid. We know that it weighs 25.0 g, and we don't know its initial temperature, which we'll call T_l. We can express Q_lost as:
Q_lost = 25.0 g * Cs_l * (65 oC - T_l)
where Cs_l is the specific heat capacity of the liquid.
Next, let's calculate the amount of heat gained by the cold water. We know that it has a mass of 350 g and an initial temperature of 45 oC. We can express Q_gained as:
Q_gained = 350 g * Cs_w * (65 oC - 45 oC)
where Cs_w is the specific heat capacity of water.
Now we can set Q_lost equal to Q_gained and solve for T_l:
25.0 g * Cs_l * (65 oC - T_l) = 350 g * Cs_w * (65 oC - 45 oC)
Dividing both sides by 25.0 g * Cs_l, we get:
65 oC - T_l = 14.545
Subtracting 14.545 from 65 oC, we get:
T_l = 50.455 oC
Therefore, the initial temperature of the liquid was 50.455 oC when it was added to the water.