Answer :
[tex]\[ \text{Final Temperature} \approx 41.11^\circ \text{C} \].[/tex] The correct answer is not among the options provided.
To find the final temperature of the mixture, we can use the principle of conservation of energy, which states that the heat lost by the hot substance (water) will be equal to the heat gained by the cold substance (ice).
The heat gained by the ice in melting and then reaching the final temperature is given by:
[tex]\[ Q_{\text{ice}} = m_{\text{ice}} \times L_f + m_{\text{ice}} \times c_{\text{ice}} \times \Delta T \][/tex]
where:
- [tex]\( m_{\text{ice}} \)[/tex] is the mass of ice,
-[tex]\( L_f \)[/tex] is the latent heat of fusion,
- [tex]\( c_{\text{ice}} \)[/tex] is the specific heat of ice, and
-[tex]\( \Delta T \)[/tex] is the change in temperature.
The heat lost by the water is given by:
[tex]\[ Q_{\text{water}} = m_{\text{water}} \times c_{\text{water}} \times \Delta T \][/tex]
Setting [tex]\( Q_{\text{ice}} = Q_{\text{water}} \) and solving for \( \Delta T \)[/tex]:
[tex]\[ m_{\text{ice}} \times L_f + m_{\text{ice}} \times c_{\text{ice}} \times \Delta T = m_{\text{water}} \times c_{\text{water}} \times \Delta T \][/tex]
Given values:
[tex]\[ 10 \, \text{g} \times 80 \, \text{cal/g} + 10 \, \text{g} \times 1 \, \text{cal/g}^\circ \text{C} \times \Delta T = 100 \, \text{g} \times 1 \, \text{cal/g}^\circ \text{C} \times \Delta T \][/tex]
Solving for [tex]\( \Delta T \)[/tex]:
[tex]\[ 800 + 10 \times \Delta T = 100 \times \Delta T \][/tex]
[tex]\[ 90 \times \Delta T = 800 \][/tex]
[tex]\[ \Delta T = \frac{800}{90} \][/tex]
[tex]\[ \Delta T \approx 8.89^\circ \text{C} \][/tex]
The final temperature is the initial temperature of the water minus [tex]\( \Delta T \):[/tex]
[tex]\[ \text{Final Temperature} = 50^\circ \text{C} - 8.89^\circ \text{C} \][/tex]
[tex]\[ \text{Final Temperature} \approx 41.11^\circ \text{C} \][/tex]
The question probable maybe:
10g of ice at o°C is mixed with 100g of water at 50°C in a calorimeter. The final temperature of the mixture is [Specific heat of water= 1 cal g¯¹°C-1, latent heat of fusion of ice= 80 cal g¯¹]
A 31.2°C
B 32.8°C
C 36.7°C
D 38.2°C
