Ch.3 Matter and Energy

Timberlake - Chemistry: An Introduction to General, Organic, and Biological Chemistry 13th Edition

Timberlake13th EditionChemistry: An Introduction to General, Organic, and Biological ChemistryISBN: 9780134421353Not the one you use?Change textbook

Timberlake 13th Edition

Ch.3 Matter and Energy

Problem 37

Chapter 3, Problem 37

If the same amount of heat is supplied to samples of 10.0 g each of aluminum, iron, and copper all at 15.0 °C, which sample would reach the highest temperature (see TABLE 3.11)?

Verified step by step guidance

Step 1: Understand the relationship between specific heat capacity and temperature change. The specific heat capacity (c) of a substance determines how much heat (q) is required to change the temperature of a given mass (m) of the substance by a certain amount (ΔT). The formula is q = m * c * ΔT.

Step 2: Recognize that the same amount of heat (q) is supplied to each sample. Since the mass (m) of each sample is the same (10.0 g), the temperature change (ΔT) will depend on the specific heat capacity (c) of each metal. Metals with lower specific heat capacities will experience a greater temperature change for the same amount of heat.

Step 3: Refer to the specific heat capacities of aluminum, iron, and copper from Table 3.11 (not provided in the image). Compare the values of specific heat capacity for these metals. Identify which metal has the lowest specific heat capacity.

Step 4: Use the relationship ΔT = q / (m * c) to confirm that the metal with the lowest specific heat capacity will reach the highest temperature when the same amount of heat is supplied.

Step 5: Conclude that the metal with the lowest specific heat capacity from Table 3.11 will reach the highest temperature. Ensure you understand the concept that lower specific heat capacity means less heat is required to increase the temperature of the substance.

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Key Concepts

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

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a crucial property that varies among different materials, influencing how quickly they heat up or cool down when subjected to the same amount of heat. Metals with lower specific heat capacities will experience a greater temperature increase when the same amount of heat is applied.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this context, when equal heat is supplied to different metals, the rate at which each metal's temperature increases depends on its specific heat capacity. Understanding heat transfer is essential for predicting how different materials respond to thermal energy.

Thermal Equilibrium

Thermal equilibrium is the state reached when two objects at different temperatures come into contact and exchange heat until they reach the same temperature. In the scenario presented, once heat is supplied to the aluminum, iron, and copper samples, they will eventually reach thermal equilibrium, but the rate at which they do so will depend on their specific heat capacities, affecting which sample reaches the highest temperature first.

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Related Practice

Textbook Question

Use the heat equation to calculate the energy, in joules and calories, for each of the following (see TABLE 3.11):

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Textbook Question

Identify each of the following changes of state as melting, freezing, sublimation, or deposition:

a. Dry ice in an ice-cream cart disappears.

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Textbook Question

Using the energy values for foods (see TABLE 3.7), determine each of the following (round off the answer for each food type to the tens place):

a. the total kilojoules in two tablespoons of crunchy peanut butter that contains 6 g of carbohydrate, 16 g of fat, and 7 g of protein

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Textbook Question

For dinner, Charles had one cup of clam chowder, which contains 16 g of carbohydrate, 12 g of fat, and 9 g of protein. How much energy, in kilocalories and kilojoules, is in the clam chowder? (Round off the answer for each food type to the tens place.)

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A patient receives 3.2 L of intravenous (IV) glucose solution. If 100. mL of the solution contains 5.0 g of glucose (carbohydrate), how many kilocalories did the patient obtain from the glucose solution?

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Textbook Question

Identify each of the following changes of state as melting, freezing, sublimation, or deposition:

b. Snow on the ground turns to liquid water.

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