A sample of copper absorbs 44 kJ of heat, resulting in a temperature rise of 65 °C. Determine the mass (in kg) of the copper sample f the specific heat capacity of copper is 0.385 J/g°C.
A sample of copper absorbs 44 kJ of heat, resulting in a temperature rise of 65 °C. Determine the mass (in kg) of the copper sample f the specific heat capacity of copper is 0.385 J/g°C.
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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A sample of copper absorbs 44 kJ of heat, resulting in a temperature rise of 65 °C. Determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g°C.
![**Problem Statement:**
A sample of copper absorbs 44 kJ of heat, resulting in a temperature rise of 65°C. Determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g°C.
**Solution Approach:**
To find the mass of the copper sample, use the formula for heat absorption:
\[ q = m \cdot c \cdot \Delta T \]
where:
- \( q \) is the heat absorbed (44,000 J, since 44 kJ = 44,000 J),
- \( m \) is the mass in grams,
- \( c \) is the specific heat capacity (0.385 J/g°C),
- \( \Delta T \) is the change in temperature (65°C).
Rearrange the formula to solve for mass \( m \):
\[ m = \frac{q}{c \cdot \Delta T} \]
Substitute the values:
\[ m = \frac{44,000 \, \text{J}}{0.385 \, \text{J/g°C} \times 65 \, \text{°C}} \]
\[ m \approx 1762.34 \, \text{g} \]
Convert the mass to kilograms:
\[ m \approx 1.762 \, \text{kg} \]
Therefore, the mass of the copper sample is approximately 1.762 kg.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f35a07c-a5eb-4d79-bb69-5908bd1ff29b%2Fc809a45f-d176-45c3-ba96-ec918dff4b87%2Ft517uzl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A sample of copper absorbs 44 kJ of heat, resulting in a temperature rise of 65°C. Determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g°C.
**Solution Approach:**
To find the mass of the copper sample, use the formula for heat absorption:
\[ q = m \cdot c \cdot \Delta T \]
where:
- \( q \) is the heat absorbed (44,000 J, since 44 kJ = 44,000 J),
- \( m \) is the mass in grams,
- \( c \) is the specific heat capacity (0.385 J/g°C),
- \( \Delta T \) is the change in temperature (65°C).
Rearrange the formula to solve for mass \( m \):
\[ m = \frac{q}{c \cdot \Delta T} \]
Substitute the values:
\[ m = \frac{44,000 \, \text{J}}{0.385 \, \text{J/g°C} \times 65 \, \text{°C}} \]
\[ m \approx 1762.34 \, \text{g} \]
Convert the mass to kilograms:
\[ m \approx 1.762 \, \text{kg} \]
Therefore, the mass of the copper sample is approximately 1.762 kg.
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