What will be the final temperature of a mixture made from 25.0 g of water at 15.0^∘ C, 45.0 g

step 1 So thermodynamics is the study of the relationship between heat, work, temperature and energy. A

What will be the final temperature of a mixture made from...

What will be the final temperature of a mixture made from $25.0 \mathrm{~g}$ of water at $15.0^{\circ} \mathrm{C}, 45.0 \mathrm{~g}$ of water at $50.0^{\circ} \mathrm{C}$, and $15.0 \mathrm{~g}$ of water at $37.0^{\circ} \mathrm{C} ?$

Key Concepts

Thermal Equilibrium

This concept refers to the state in which all interacting systems or parts of a system have reached the same temperature, meaning there is no net transfer of heat between them. In the context of mixing substances, thermal equilibrium is the point at which the heat exchange process ends, and all substances achieve a uniform temperature.

Conservation of Energy

In closed systems where no energy is lost to the surroundings, the total energy remains constant. When different substances at varying temperatures are mixed, the heat lost by the warmer substances exactly equals the heat gained by the cooler ones. This principle is used to determine the final equilibrium temperature of the mixture, ensuring that the overall energy balance is maintained.

Specific Heat Capacity

This is a property of a material that indicates the amount of heat required to change the temperature of a unit mass of the substance by one degree. In calorimetry problems involving mixtures, specific heat capacity helps quantify how much energy is absorbed or released by each component during the temperature change, which is essential for calculating the resultant equilibrated temperature.

Weighted Average Temperature

When different masses of a substance, each at a different temperature, are mixed together, the final equilibrium temperature can be determined by a weighted average. Here, the weight of each component is its mass, and the temperatures are averaged proportionally to the masses. This concept ensures that components with a larger mass have a greater influence on the final temperature.

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