6. Suppose you had 1.0g and 3.0g samples of zinc metal. Compare the amount of energy required to raise the temperature of each sample by the same amount. Explain.
6. Suppose you had 1.0g and 3.0g samples of zinc metal. Compare the amount of energy required to raise the temperature of each sample by the same amount. Explain.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Question 6: Energy Requirement for Zinc Samples**
**Problem Statement:**
Suppose you had 1.0g and 3.0g samples of zinc metal. Compare the amount of energy required to raise the temperature of each sample by the same amount. Explain.
**Explanation:**
The amount of energy required to raise the temperature of an object can be calculated using the formula:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat energy (in joules),
- \( m \) is the mass of the sample (in grams),
- \( c \) is the specific heat capacity of the material (in joules per gram per degree Celsius),
- \( \Delta T \) is the change in temperature (in degrees Celsius).
For this problem:
- Both samples are zinc, so the specific heat capacity \( c \) is the same for both samples.
- The change in temperature \( \Delta T \) is the same for both samples.
Given:
- Sample 1: 1.0g of zinc,
- Sample 2: 3.0g of zinc.
Since the specific heat capacity \( c \) and the temperature change \( \Delta T \) are constant for both samples, the energy \( Q \) is directly proportional to the mass \( m \).
**Energy Calculation:**
For the 1.0g sample:
\[ Q_1 = (1.0g) \times c \times \Delta T \]
For the 3.0g sample:
\[ Q_2 = (3.0g) \times c \times \Delta T \]
Since the mass of the second sample is three times that of the first sample, the energy required to raise the temperature of the 3.0g sample by the same amount will also be three times as much.
**Conclusion:**
The 3.0g sample of zinc requires three times more energy than the 1.0g sample to achieve the same temperature increase. This is because the energy required is directly proportional to the mass when the material and temperature change are the same.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff99b38db-8b1e-4ff4-bf9f-2b903450ffb8%2F097fce33-c8ba-4b81-a05d-8980b1875515%2Fd2joex_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 6: Energy Requirement for Zinc Samples**
**Problem Statement:**
Suppose you had 1.0g and 3.0g samples of zinc metal. Compare the amount of energy required to raise the temperature of each sample by the same amount. Explain.
**Explanation:**
The amount of energy required to raise the temperature of an object can be calculated using the formula:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat energy (in joules),
- \( m \) is the mass of the sample (in grams),
- \( c \) is the specific heat capacity of the material (in joules per gram per degree Celsius),
- \( \Delta T \) is the change in temperature (in degrees Celsius).
For this problem:
- Both samples are zinc, so the specific heat capacity \( c \) is the same for both samples.
- The change in temperature \( \Delta T \) is the same for both samples.
Given:
- Sample 1: 1.0g of zinc,
- Sample 2: 3.0g of zinc.
Since the specific heat capacity \( c \) and the temperature change \( \Delta T \) are constant for both samples, the energy \( Q \) is directly proportional to the mass \( m \).
**Energy Calculation:**
For the 1.0g sample:
\[ Q_1 = (1.0g) \times c \times \Delta T \]
For the 3.0g sample:
\[ Q_2 = (3.0g) \times c \times \Delta T \]
Since the mass of the second sample is three times that of the first sample, the energy required to raise the temperature of the 3.0g sample by the same amount will also be three times as much.
**Conclusion:**
The 3.0g sample of zinc requires three times more energy than the 1.0g sample to achieve the same temperature increase. This is because the energy required is directly proportional to the mass when the material and temperature change are the same.
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