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 45.9 g of this metal, initially at 20.0 °C? Tinal = °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 45.9 g of this metal, initially at 20.0 °C? Tinal = °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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![**Problem Statement:**
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 45.9 g of this metal, initially at 20.0 °C?
**Solution:**
To find the final temperature (\( T_{\text{final}} \)), use the formula for heat transfer:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the heat added (305 J),
- \( m \) is the mass of the metal (45.9 g),
- \( c \) is the specific heat capacity (0.128 J/(g·°C)),
- \( \Delta T \) is the change in temperature (\( T_{\text{final}} - T_{\text{initial}} \)).
We can rearrange the equation to solve for \( T_{\text{final}} \):
\[ T_{\text{final}} = T_{\text{initial}} + \frac{q}{m \cdot c} \]
Substitute the values into the equation:
\[ T_{\text{final}} = 20.0 °C + \frac{305 \, \text{J}}{45.9 \, \text{g} \cdot 0.128 \, \text{J/(g·°C)}} \]
Calculate to find \( T_{\text{final}} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cab08ae-8e5c-4fa2-a89b-725536e38ab3%2F754ebbe1-97b2-4ec4-9aa4-dd2ba7cca629%2Fycv5ytm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
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 45.9 g of this metal, initially at 20.0 °C?
**Solution:**
To find the final temperature (\( T_{\text{final}} \)), use the formula for heat transfer:
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( q \) is the heat added (305 J),
- \( m \) is the mass of the metal (45.9 g),
- \( c \) is the specific heat capacity (0.128 J/(g·°C)),
- \( \Delta T \) is the change in temperature (\( T_{\text{final}} - T_{\text{initial}} \)).
We can rearrange the equation to solve for \( T_{\text{final}} \):
\[ T_{\text{final}} = T_{\text{initial}} + \frac{q}{m \cdot c} \]
Substitute the values into the equation:
\[ T_{\text{final}} = 20.0 °C + \frac{305 \, \text{J}}{45.9 \, \text{g} \cdot 0.128 \, \text{J/(g·°C)}} \]
Calculate to find \( T_{\text{final}} \).
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