Table of contents

1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
8. Gases, Liquids and Solids3h 25m
9. Solutions4h 10m
10. Acids and Bases3h 29m
11. Nuclear Chemistry56m
BONUS: Lab Techniques and Procedures1h 38m
BONUS: Mathematical Operations and Functions47m
12. Introduction to Organic Chemistry1h 34m
13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
17. Amines39m
18. Amino Acids and Proteins1h 51m
19. Enzymes1h 37m
20. Carbohydrates1h 41m
21. The Generation of Biochemical Energy2h 8m
22. Carbohydrate Metabolism2h 22m
23. Lipids2h 26m
24. Lipid Metabolism1h 45m
25. Protein and Amino Acid Metabolism1h 37m
26. Nucleic Acids and Protein Synthesis2h 54m

7. Energy, Rate and Equilibrium

Heat Capacity

GOB Chemistry

7. Energy, Rate and Equilibrium

Heat Capacity

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3:32 minutes

Problem 109

Textbook Question

An archeologist finds a 1.62 kg goblet that she believes to be made of pure gold. When 1350 cal (5650 J) of heat is added to the goblet, its temperature increases by 7.8 ℃. Calculate the specific heat of the goblet. Is it made of gold? Explain.

Verified step by step guidance

Step 1: Recall the formula for specific heat capacity:

c = Q / (m · ΔT)

, where

c

is the specific heat capacity,

Q

is the heat added,

m

is the mass of the object, and

ΔT

is the change in temperature.

Step 2: Identify the given values from the problem:

Q = 5650 \, J

m = 1.62 \, kg

, and

ΔT = 7.8 \, ^\circ C

Step 3: Substitute the given values into the formula:

c = 5650 / (1.62 · 7.8)

. Perform the division and multiplication in the denominator to simplify the expression.

Step 4: Compare the calculated specific heat capacity to the known specific heat capacity of gold, which is approximately

0.129 \, J/(g · ^\circ C)

129 \, J/(kg · ^\circ C)

. This will help determine if the goblet is made of pure gold.

Step 5: Conclude whether the goblet is made of gold based on how closely the calculated specific heat matches the known value for gold. If the values differ significantly, the goblet is not pure gold.

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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 kilogram of a substance by one degree Celsius. It is a material property that varies between different substances, allowing us to identify materials based on how they respond to heat. The formula to calculate specific heat is Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat, and ΔT is the change in temperature.

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 scenario, the heat added to the goblet causes its temperature to rise, which can be quantified to determine the specific heat. Understanding heat transfer is crucial for analyzing how materials behave under thermal conditions and for making comparisons between different substances.

Material Identification

Material identification involves determining the composition of a substance based on its physical and thermal properties. In this case, by calculating the specific heat of the goblet and comparing it to known values for pure gold (approximately 0.129 J/g°C), we can assess whether the goblet is indeed made of gold. This process is essential in fields like archaeology and materials science for verifying the authenticity of artifacts.

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Textbook Question

On a hot day, the beach sand gets hot but the water stays cool. Would you predict that the specific heat of sand is higher or lower than that of water? Explain.

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Textbook Question

A metal is thought to be titanium or aluminum. When 4.7 g of the metal absorbs 11 J, its temperature rises by 4.5 °C.

b. Would you identify the metal as titanium or aluminum (see TABLE 3.11)?

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Textbook Question

A metal is thought to be copper or gold. When 18 g of the metal absorbs 58 cal, its temperature rises by 35 °C.

a. What is the specific heat, in cal/g °C, of the metal?

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Textbook Question

When 1.0 tablespoon of butter is burned or used by our body, it releases 100 kcal (100 food Calories or 418.4 kJ) of energy. If we could use all the energy provided, how many tablespoons of butter would have to be burned to raise the temperature of 3.00 L of water from 18.0 ℃ to 90.0 ℃

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Multiple Choice

A sample of copper absorbs 3.53 kJ of heat, which increases the temperature by 25 ºC, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J / g  ºC.

Based on their given specific heat capacities which compound would show the greatest temperature change upon absorbing 25.0 J of heat?

50.00 g of heated metal ore is placed into an insulated beaker containing 822.5 g of water. Once the metal heats up the final temperature of the water is 32.08 ºC. If the metal gains 14.55 kJ of energy, what is the initial temperature of the water? The specific heat capacity of copper is 4.184 J / g  ºC.

Assuming that Coca-Cola has the same specific heat as water, how much energy in calories is removed when 350 g of Coca-Cola (about the contents of one 12 oz can) is cooled from room temperature (25 °C) to refrigerator temperature (3 °C)?

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