Water Our Lifeline

Step 1: Use the principle of conservation of heat energy.

When two bodies of water at different temperatures are mixed, heat flows from the hotter body to the cooler body until thermal equilibrium is reached. The heat lost by the hotter water equals the heat gained by the cooler water:

where:

• and are the masses of the two bodies of water,
• is the specific heat capacity of water (same for both), and
• and are the changes in temperature for the two bodies.

Step 2: Set up the equation.

Let the final temperature of the mixture be . For the hotter water ( at ):

For the cooler water ( at ):

Substitute into the heat balance equation:

Step 3: Solve for .

Expand both sides:

Rearrange terms:

Solve for :

Step 4: Compare with the options.

The final temperature ( ) is less than .

Final Answer: The final temperature is , which corresponds to option .