An aluminum cup of mass 200 g contains 800 g of water in thermal equilibrium at 80.0^∘ C . The c

step 1 The expression for the heat energy required to change the temperature of the substance is Q is M

An aluminum cup of mass 200 g contains 800 g of water in...

An aluminum cup of mass 200 $\mathrm{g}$ 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 by $1.50^{\circ} \mathrm{C}$ per minute. At what rate is energy being removed by heat? Express your answer in watts.

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Key Concepts

Specific Heat Capacity

This property represents the amount of energy required to raise the temperature of a unit mass of a substance by one degree. It is crucial in calculating the energy change in a system as different materials respond differently to heat depending on their specific heat capacity.

Heat Energy Calculation

Heat energy can be calculated using the formula Q = mc?T, where m is mass, c is the specific heat capacity, and ?T is the change in temperature. This calculation is essential for determining the total amount of heat energy removed or added during a temperature change in any system.

Rate of Heat Transfer

The rate of heat transfer is defined as the amount of energy per unit time that is being transferred, often expressed in watts. It is calculated by dividing the total heat energy change by the time period over which the change occurs, linking thermal processes to power and energy flow.

Unit Conversion

Accurate calculations in heat transfer problems require consistent units, such as converting time from minutes to seconds or mass between different units. Proper unit conversion ensures that the derived quantities like energy and power are expressed correctly in standard units such as joules and watts.

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