10 g of aluminum at 200°C and 20 g of copper are dropped into 50 cm3 of ethyl alcohol at 15°C. The temperature quickly comes to 25°C. What was the initial temperature of the copper?

Ch 19: Work, Heat, and the First Law of Thermodynamics

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 19: Work, Heat, and the First Law of Thermodynamics

Problem 78

Chapter 19, Problem 78

10 g of aluminum at 200°C and 20 g of copper are dropped into 50 cm³ of ethyl alcohol at 15°C. The temperature quickly comes to 25°C. What was the initial temperature of the copper?

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Identify the principle of conservation of energy: The heat lost by the aluminum and copper will equal the heat gained by the ethyl alcohol, assuming no heat is lost to the surroundings.

Write the heat transfer equation for each material: For aluminum and copper, the heat lost is given by $ Q = m c \Delta T $, and for ethyl alcohol, the heat gained is also $ Q = m c \Delta T $.

Express the heat transfer for each material: For aluminum, $ Q_{Al} = m_{Al} c_{Al} (T_{Al,initial} - T_{final}) $; for copper, $ Q_{Cu} = m_{Cu} c_{Cu} (T_{Cu,initial} - T_{final}) $; and for ethyl alcohol, $ Q_{EA} = m_{EA} c_{EA} (T_{final} - T_{EA,initial}) $.

Set up the energy conservation equation: $ Q_{Al} + Q_{Cu} = Q_{EA} $. Substitute the expressions for $ Q $ from the previous step into this equation.

Solve for the initial temperature of copper $ T_{Cu,initial} $: Rearrange the equation to isolate $ T_{Cu,initial} $, substituting the known values for masses, specific heats, and temperatures. Be sure to convert the volume of ethyl alcohol to mass using its density.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat Transfer

Heat transfer is the process of thermal energy moving from one object to another due to a temperature difference. In this scenario, heat flows from the aluminum and copper to the ethyl alcohol until thermal equilibrium is reached. Understanding how heat is exchanged is crucial for solving problems involving temperature changes in different materials.

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. Each material has a unique specific heat capacity, which affects how much its temperature changes when heat is added or removed. This concept is essential for calculating the final temperatures of the aluminum, copper, and ethyl alcohol in the given problem.

Thermal Equilibrium

Thermal equilibrium occurs when two or more bodies in thermal contact reach the same temperature, resulting in no net heat flow between them. In this problem, the aluminum, copper, and ethyl alcohol reach a common temperature of 25°C. Understanding thermal equilibrium helps in applying the principle of conservation of energy to find unknown initial temperatures.

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