A biology experiment requires the preparation of a water...

A biology experiment requires the preparation of a water bath at $37.0^{\circ} \mathrm{C}$ (body temperature). The temperature of the cold tap water is $22.0^{\circ} \mathrm{C}$, and the temperature of the hot tap water is $55.0^{\circ} \mathrm{C}$. If a student starts with $90.0 \mathrm{~g}$ cold water, what mass of hot water must be added to reach $37.0^{\circ} \mathrm{C} ?$

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Key Concepts

Thermal Equilibrium

Thermal equilibrium is the state where two or more substances reach a uniform temperature through the exchange of heat. This concept is fundamental in mixtures, as it explains how a system achieves balance by transferring heat until all parts of the system have the same temperature.

Conservation of Energy in Heat Transfer

This principle dictates that in an isolated system, the total energy remains constant. When mixing substances at different temperatures, the heat lost by the warmer substance must equal the heat gained by the cooler substance, allowing for the calculation of unknown quantities such as mass or temperature.

Specific Heat Capacity

Specific heat capacity quantifies the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. In problems involving the heating or cooling of substances, this property helps determine how much heat is absorbed or released during temperature changes.

Weighted Average Temperature

The concept of a weighted average temperature is used when combining substances with different temperatures. By considering the mass and temperature of each substance, the final equilibrium temperature can be calculated as a weighted average, which is especially useful in solving mixing problems.

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