One beaker contains 156 g of water at 22^∘ C, and a second beaker contains 85.2 g of water at 95

step 1 For this problem, two bodies of water are added to each other, so the specific features are the

One beaker contains 156 g of water at 22^∘ C, and a second...

One beaker contains 156 g of water at $22^{\circ} \mathrm{C},$ and a second beaker contains $85.2 \mathrm{g}$ of water at $95^{\circ} \mathrm{C}$ The water in the two beakers is mixed. What is the final water temperature?

Key Concepts

Thermal Equilibrium

Thermal equilibrium refers to the state reached when two substances at different temperatures, upon coming into contact, exchange heat until they achieve the same temperature. This concept is based on the principle that heat will flow from the hotter substance to the cooler one until no temperature gradient exists between them.

Conservation of Energy

The conservation of energy principle states that in an isolated system, energy cannot be created or destroyed, only transferred or converted from one form to another. In the context of heat transfer during mixing, the heat lost by the warmer substance is equal to the heat gained by the cooler substance, assuming no external losses.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. This property is essential in calculating how much heat energy is transferred between substances, since different materials require different amounts of energy to change temperature.

Weighted Average Temperature

The weighted average temperature is used to determine the final equilibrium temperature when mixing substances of different masses and temperatures. By weighting each temperature by the mass and specific heat capacity of the substance, one can calculate a final temperature that accounts for the differing contributions of each component.

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