Get personalized and accurate responses to your questions with IDNLearn.com. Discover comprehensive answers to your questions from our community of experienced professionals.
Sagot :
Answer:
[tex]\( 30 \, \text{J/C} \)[/tex]
Explanation:
The heat lost by the hot water is equal to the heat gained by the cold water plus the heat absorbed by the calorimeter. The calorimeter constant represents the heat capacity of the calorimeter.
Solving:
Formula for hot water:
[tex]q_{\text{hot}} = m_{\text{hot}} \cdot c_{\text{water}} \cdot (T_{\text{initial, hot}} - T_{\text{final}})[/tex]
[tex]\hrulefill[/tex]
Given:
[tex]\item \( m_{\text{hot}} = 50 \, \text{ml} = 50 \, \text{g} \) (The density of water is \( 1 \, \text{g/ml}) \ \item \( c_{\text{water}} = 4.18 \, \text{J/g*C} \) (specific heat capacity of water) \item \( T_{\text{initial, hot}} = 85 \, \text{C} \) \item \( T_{\text{final}} = 53 \, \text{C} \)[/tex]
[tex]\hrulefill[/tex]
[tex]q_{\text{hot}} = 50 \, \text{g} \cdot 4.18 \, \text{J/gC} \cdot (85 \, \text{C} - 53 \, \text{C})\\ \\ q_{\text{hot}} = 50 \cdot 4.18 \cdot 32\\\\ \boxed{q_{\text{hot}} = 6692 \, \text{J}\\}[/tex]
[tex]\hrulefill[/tex]
Formula for cold water:
[tex]\[ q_{\text{cold}} = m_{\text{cold}} \cdot c_{\text{water}} \cdot (T_{\text{final}} - T_{\text{initial, cold}}) \][/tex]
[tex]\hrulefill[/tex]
Given:
[tex]\item \( m_{\text{cold}} = 50 \, \text{ml} = 50 \, \text{g} \) \item \( T_{\text{initial, cold}} = 25 \, \text{C} \)[/tex]
[tex]\hrulefill[/tex]
[tex]q_{\text{cold}} = 50 \, \text{g} \cdot 4.18 \, \text{J/gC} \cdot (53 \, \text{C} - 25 \, \text{C})\\ q_{\text{cold}} = 50 \cdot 4.18 \cdot 28\\ \boxed{q_{\text{cold}} = 5852 \, \text{J}}[/tex]
[tex]\hrulefill[/tex]
Calorimeter constant:
[tex]\[ C_{\text{cal}} = \frac{q_{\text{cal}}}{\Delta T} \] \\\\ Where \( \Delta T \) is the change in temperature of the water, which is the same for both hot and cold water: \[[/tex]
[tex]\hrulefill[/tex]
[tex]\Delta T = T_{\text{final}} - T_{\text{initial, cold}} = 53 \, \text{C} - 25 \, \text{C} = 28 \, \text{C} \\ C_{\text{cal}} = \frac{840 \, \text{J}}{28 \, \text{C}}\\ \boxed{ C_{\text{cal}} = 30 \, \text{J/C}}[/tex]
[tex]\hrulefill[/tex]
[tex]\text{Therefore, the calorimeter constant is \( 30 \, \text{J/C} \).}[/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.
