Questions: 10.0 g Cu was heated to 600°C then dropped into water at 25°C If gow hod 325 g water what is the final temp. Cω=0.385 S / g°C C4.0=4.184 J / g°C

10.0 g Cu was heated to 600°C then dropped into water at 25°C

If gow hod 325 g water what is the final temp.

Cω=0.385 S / g°C
C4.0=4.184 J / g°C
Transcript text: 10.0 g . Cu was heated to $600^{\circ} \mathrm{C}$ then dropped into water at $25^{\circ} \mathrm{C}$ If gow hod 325 g . water what is the final temp. \[ \begin{array}{l} C_{\omega}=0.385 \mathrm{~S} / \mathrm{g}^{\circ} \mathrm{C} \\ C_{4.0}=4.184 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C} \end{array} \]
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Solution

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Solution Steps

Step 1: Identify the Known Values

We are given the following information:

  • Mass of copper, mCu=10.0g m_{\text{Cu}} = 10.0 \, \text{g}
  • Initial temperature of copper, TCu, initial=600C T_{\text{Cu, initial}} = 600^\circ \text{C}
  • Mass of water, mwater=325g m_{\text{water}} = 325 \, \text{g}
  • Initial temperature of water, Twater, initial=25C T_{\text{water, initial}} = 25^\circ \text{C}
  • Specific heat capacity of copper, CCu=0.385J/gC C_{\text{Cu}} = 0.385 \, \text{J/g}^\circ \text{C}
  • Specific heat capacity of water, Cwater=4.184J/gC C_{\text{water}} = 4.184 \, \text{J/g}^\circ \text{C}
Step 2: Set Up the Heat Transfer Equation

When the copper is dropped into the water, heat will transfer from the copper to the water until thermal equilibrium is reached. The heat lost by the copper will equal the heat gained by the water:

mCuCCu(TfinalTCu, initial)=mwaterCwater(TfinalTwater, initial) m_{\text{Cu}} \cdot C_{\text{Cu}} \cdot (T_{\text{final}} - T_{\text{Cu, initial}}) = -m_{\text{water}} \cdot C_{\text{water}} \cdot (T_{\text{final}} - T_{\text{water, initial}})

Step 3: Solve for the Final Temperature

Substitute the known values into the equation:

10.00.385(Tfinal600)=3254.184(Tfinal25) 10.0 \cdot 0.385 \cdot (T_{\text{final}} - 600) = -325 \cdot 4.184 \cdot (T_{\text{final}} - 25)

Simplify and solve for Tfinal T_{\text{final}} :

3.85(Tfinal600)=1358.8(Tfinal25) 3.85 \cdot (T_{\text{final}} - 600) = -1358.8 \cdot (T_{\text{final}} - 25)

Expanding both sides:

3.85Tfinal2310=1358.8Tfinal+33970 3.85T_{\text{final}} - 2310 = -1358.8T_{\text{final}} + 33970

Combine like terms:

3.85Tfinal+1358.8Tfinal=33970+2310 3.85T_{\text{final}} + 1358.8T_{\text{final}} = 33970 + 2310

1362.65Tfinal=36280 1362.65T_{\text{final}} = 36280

Solve for Tfinal T_{\text{final}} :

Tfinal=362801362.6526.625C T_{\text{final}} = \frac{36280}{1362.65} \approx 26.625^\circ \text{C}

Final Answer

The final temperature of the system is 26.63C\boxed{26.63^\circ \text{C}}.

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