An aluminum cup with a mass of 200 g contains 800 g of...

An aluminum cup with a mass of 200 g contains $800 \mathrm{~g}$ of water in thermal equilibrium at $80.0^{\circ} \mathrm{C}$. The combination of cup and water is cooled uniformly so that the temperature decreases at a rate of $1.50^{\circ} \mathrm{C} / \mathrm{min} .$ At what rate is energy being removed by heat? Express your answer in watts.

Key Concepts

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 (or one Kelvin). It is a material-specific property that indicates how quickly a substance can gain or lose heat, and it plays a crucial role in quantifying energy changes in thermal processes.

Combined Heat Capacity

In systems made up of different substances, each with its own mass and specific heat capacity, the total heat capacity is calculated by summing the products of mass and specific heat capacity for each component. This aggregate value represents the amount of energy needed to change the temperature of the entire system uniformly.

Rate of Energy Transfer (Power)

The rate of energy transfer, often measured in watts (joules per second), reflects how quickly energy is removed from or delivered to a system. It is determined by the product of the system’s total heat capacity and the rate of temperature change, linking thermal dynamics directly to power considerations.

Unit Conversion in Thermal Dynamics

Accurate calculations in thermal dynamics often require unit conversion, such as converting temperature change rates from degrees per minute to degrees per second. This ensures that the computed energy transfer rates are expressed in compatible units, such as watts, where one watt corresponds to one joule per second.

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