A 200-g aluminum cup contains 800 g of water in thermal equilibrium with the cup at 80^∘ C. The

step 1 In this problem, the amount of heat removed from the system is given by this equation. So let's

A 200-g aluminum cup contains 800 g of water in thermal...

A 200-g aluminum cup contains $800 \mathrm{~g}$ of water in thermal equilibrium with the cup at $80^{\circ} \mathrm{C}$. The combination of cup and water is cooled uniformly so that the temperature decreases by $1.5^{\circ} \mathrm{C}$ per minute. At what rate is energy being removed? Express your answer in watts.

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Key Concepts

Specific Heat Capacity

This concept describes the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a fundamental property of materials that indicates how resistant a substance is to temperature changes when energy is added or removed.

Heat Capacity

Heat capacity is the total amount of energy needed to change an object’s temperature by a given amount. For composite systems, such as a container with a liquid, the overall heat capacity is determined by summing the contributions of each component, each calculated as the product of its mass and specific heat capacity.

Thermal Equilibrium

Thermal equilibrium refers to the state in which all parts of a system have reached the same temperature, meaning there is no net flow of thermal energy within the system. It serves as a starting point for analyzing energy changes when the system is subjected to external heating or cooling.

Rate of Energy Transfer

The rate of energy transfer, often measured in watts (joules per second), quantifies how quickly energy is being added to or removed from a system. In thermal processes, this rate is determined by the product of the overall heat capacity of the system and the rate at which the temperature changes, connecting energy flow directly with changes in temperature over time.

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