Without considering the containing vessel, what mass of boiled water can raise the temperature of 8 kg of…

To solve this problem, we use the Principle of Conservation of Heat Energy (also known as the Method of Mixtures). This principle states that:

Heat Lost by Hot Water = Heat Gained by Cold Water

1. Analyze the Question

• Cold Water: Mass ($m_1$) = 8 kg, Initial Temperature ($T_1$) = 25°C.
• Hot Water: Mass ($m_2$) = ?, Initial Temperature ($T_2$) = 100°C (Since it is "boiled water," we assume its temperature is 100°C).
• Final Mixture Temperature ($T_f$): 60°C.
• Specific Heat Capacity ($c$): Since both substances are water, the specific heat capacity ($c$) is the same for both and will cancel out in the equation.

2. Explain the Concept

The formula for heat exchange is:

Where:

• $m$ = mass
• $c$ = specific heat capacity
• $\Delta\theta$ = change in temperature

3. Show the Solution

Step 1: Calculate heat gained by the cold water:

Step 2: Calculate heat lost by the hot water:

Step 3: Equate Heat Lost to Heat Gained:

Divide both sides by $c$ (since it is common to both):

4. Identify the Answer

Comparing our result to the given options, the correct mass is 7 kg.

5. Exam Tip

In calorimetry problems involving the same substance (like water mixed with water), you can always ignore the specific heat capacity ($c$) because it appears on both sides of the equation and cancels out. This saves you time during the exam! Also, always remember that "boiled water" is a standard code in physics problems for 100°C.