The specific heat of a certain type of metal is 0.128 J/(g-°C). What is the final temperature if 305 J of heat is added to 28.0 g of this metal, initially at 20.0 °C? Tfinal = 59.0 mpt Incorrect 'C
The specific heat of a certain type of metal is 0.128 J/(g-°C). What is the final temperature if 305 J of heat is added to 28.0 g of this metal, initially at 20.0 °C? Tfinal = 59.0 mpt Incorrect '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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![The problem presented on the educational website is as follows:
"The specific heat of a certain type of metal is 0.128 J/(g°C). What is the final temperature if 305 J of heat is added to 28.0 g of this metal, initially at 20.0 °C?"
There is an interactive box for entering the answer, labeled as "T_final = _____ °C". An answer of "59.0 °C" was entered but marked as incorrect.
### Explanation:
To calculate the final temperature, we can use the formula for heat transfer:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the amount of heat added (305 J),
- \( m \) is the mass of the metal (28.0 g),
- \( c \) is the specific heat capacity (0.128 J/(g°C)),
- \( \Delta T \) is the change in temperature (\( T_{\text{final}} - T_{\text{initial}} \)).
Rearranging the formula to solve for \( T_{\text{final}} \):
\[ T_{\text{final}} = \frac{q}{m \cdot c} + T_{\text{initial}} \]
Substituting the given values:
\[ T_{\text{final}} = \frac{305 \, \text{J}}{28.0 \, \text{g} \cdot 0.128 \, \text{J/(g°C)}} + 20.0\, \text{°C} \]
Calculating the final temperature will provide the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc195bb-9009-47db-866e-65b6514806e8%2F1bff7c69-a7f8-4ec0-8883-9e5bacd42bb3%2Fqlhmaeo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem presented on the educational website is as follows:
"The specific heat of a certain type of metal is 0.128 J/(g°C). What is the final temperature if 305 J of heat is added to 28.0 g of this metal, initially at 20.0 °C?"
There is an interactive box for entering the answer, labeled as "T_final = _____ °C". An answer of "59.0 °C" was entered but marked as incorrect.
### Explanation:
To calculate the final temperature, we can use the formula for heat transfer:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the amount of heat added (305 J),
- \( m \) is the mass of the metal (28.0 g),
- \( c \) is the specific heat capacity (0.128 J/(g°C)),
- \( \Delta T \) is the change in temperature (\( T_{\text{final}} - T_{\text{initial}} \)).
Rearranging the formula to solve for \( T_{\text{final}} \):
\[ T_{\text{final}} = \frac{q}{m \cdot c} + T_{\text{initial}} \]
Substituting the given values:
\[ T_{\text{final}} = \frac{305 \, \text{J}}{28.0 \, \text{g} \cdot 0.128 \, \text{J/(g°C)}} + 20.0\, \text{°C} \]
Calculating the final temperature will provide the correct answer.
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